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Marklund, Lars. "Topographic Control of Groundwater Flow." Doctoral thesis, KTH, Mark- och vattenteknik, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-11153.
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Gravity is the main driving force for groundwater flow, and both landscape topography and geology distribute the effects of gravity on groundwater flow. The groundwater table defines the distribution of the potential energy of the water. In humid regions where the bedrock permeability is relatively low and the soil depth is sufficiently shallow, the groundwater table closely follows the landscape topography and, thus, the topography controls the groundwater circulation in these regions. In this thesis, I investigate multi-scale topography-controlled groundwater flow, with the goal of systematizing the spatial distribution of groundwater flow and assessing geological parameters of importance for groundwater circulation. Both exact solutions and numerical models are utilized for analyzing topography-controlled groundwater flow. The more complex numerical models are used to explore the importance of various simplifications of the exact solutions. The exact solutions are based on spectral representation of the topography and superpositioning of unit solutions to the groundwater flow field. This approach is an efficient way to analyze multi-scaled topography-controlled groundwater flow because the impact of individual topographic scales on the groundwater flow can be analyzed separately. The results presented here indicate that topography is fractal and affects groundwater flow cells at wide range of spatial scales. We show that the fractal nature of the land surface produces fractal distributions of the subsurface flow patterns. This underlying similarity in hydrological processes also yields a single scale-independent distribution of subsurface water residence times which have been found in distributions of solute efflux from watersheds. Geological trends modify the topographic control of the groundwater circulation pattern and this thesis presents exact solutions explaining the impact of geological layering, depth-decaying and anisotropic hydraulic conductivity on the groundwater flow field. For instance, layers of Quaternary deposits and decaying permeability with depth both increase the importance of smaller topographic scales and creates groundwater flow fields where a larger portion of the water occupies smaller and shallower circulation cells, in comparison to homogeneous systems.<br>Gravitationen är den mest betydelsefulla drivkraften för grundvattenströmning. Topografin och geologin fördelar vattnets potentiella energi i landskapet. Grundvattenytans läge definierar vattnets potentiella energi, vilket är ett randvillkor för grundvattnets strömningsfält. I humida områden med en relativt tät berggrund och tillräckligt tunna jordlager, följer grundvattenytan landskapets topografi. Därav följer att grundvattenströmningen är styrd av topografin i dessa områden. I denna avhandling belyser jag den flerskaliga topografistyrda grundvattenströmningen. Min målsättning har varit att kvantitativt bestämma grundvattenströmningens rumsliga fördelning samt att undersöka hur olika geologiska parametrar påverkar grundvattencirkulationen. Jag har använt såväl numeriska modeller som analytiska lösningar, för att undersöka hur topografin styr grundvattenströmningen. De numeriska modellerna är mer komplexa än de analytiska lösningarna och kan därför användas för att undersöka betydelserna av olika förenklingar som finns i de analytiska lösningarna. De analytiska lösningarna är baserade på spektralanalys av topografin, samt superponering av enhetslösningar, där varje enhetslösning beskriver hur en specifik topografisk skala påverkar grundvattnets strömningsfält. Detta är ett effektivt tillvägagångssätt för att undersöka flerskaliga effekter av topografin, eftersom påverkan av varje enskild topografisk skala kan studeras separat. Resultaten som presenteras indikerar att topografin är fraktal och att den ger upphov till cirkulationsceller av varierande storlek som även dessa är av en fraktal natur. Denna grundläggande fördelning i grundvattnets strömningsfält ger upphov till att grundvattnets uppehållstid i marken följer ett självlikformigt mönster och kan förklara uppmätta tidsvariationer av lösta ämnens koncentrationer i vattendrag efter regn. Geologiska trender påverkar hur grundvattenströmningen styrs av topografin. De exakta lösningar som presenteras här, beskriver hur geologiska lager samt djupavtagande och anisotropisk hydraulisk konduktivitet påvekar grundvattnets strömning. Exempelvis är betydelsen av mindre topografiska skalor viktigare i områden med kvartära avlagringar och en berggrund med djupavtagande konduktivitet, än i områden med homogen bergrund utan kvartära avlagringar. Dessutom är en större andel strömmande vatten belägen närmare markytan i de förstnämnda områdena.<br>QC 20100802
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Holt, Jason Tempest. "Topographic influences on Kelvin-Helmholtz instability." Thesis, University of Southampton, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.295515.
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Marks, Kathryn Jean. "Enhanced flood hydraulic modelling using topographic remote sensing." Thesis, University of Bristol, 2001. http://hdl.handle.net/1983/e9866673-d6aa-49b5-964c-ed984940801c.
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Wichura, Henry. "Topographic evolution of the East African Plateau : a combined study on lava-flow modeling and paleo-topography." Phd thesis, Universität Potsdam, 2011. http://opus.kobv.de/ubp/volltexte/2011/5236/.
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The East African Plateau provides a spectacular example of geodynamic plateau uplift, active continental rifting, and associated climatic forcing. It is an integral part of the East African Rift System and has an average elevation of approximately 1,000 m. Its location coincides with a negative Bouguer gravity anomaly with a semi-circular shape, closely related to a mantle plume, which influences the Cenozoic crustal development since its impingement in Eocene-Oligocene time.
The uplift of the East African Plateau, preceding volcanism, and rifting formed an important orographic barrier and tectonically controlled environment, which is profoundly influenced by climate driven processes. Its location within the equatorial realm supports recently proposed hypotheses, that topographic changes in this region must be considered as the dominant forcing factor influencing atmospheric circulation patterns and rainfall distribution. The uplift of this region has therefore often been associated with fundamental climatic and environmental changes in East Africa and adjacent regions. While the far-reaching influence of the plateau uplift is widely accepted, the timing and the magnitude of the uplift are ambiguous and are still subject to ongoing discussion. This dilemma stems from the lack of datable, geomorphically meaningful reference horizons that could record surface uplift.
In order to quantify the amount of plateau uplift and to find evidence for the existence of significant relief along the East African Plateau prior to rifting, I analyzed and modeled one of the longest terrestrial lava flows; the 300-km-long Yatta phonolite flow in Kenya. This lava flow is 13.5 Ma old and originated in the region that now corresponds to the eastern rift shoulders. The phonolitic flow utilized an old riverbed that once drained the eastern flank of the plateau. Due to differential erosion this lava flow now forms a positive relief above the parallel-flowing Athi River, which is mimicking the course of the paleo-river.
My approach is a lava-flow modeling, based on an improved composition and temperature dependent method to parameterize the flow of an arbitrary lava in a rectangular-shaped channel. The essential growth pattern is described by a one-dimensional model, in which Newtonian rheological flow advance is governed by the development of viscosity and/or velocity in the internal parts of the lava-flow front. Comparing assessments of different magma compositions reveal that length-dominated, channelized lava flows are characterized by high effusion rates, rapid emplacement under approximately isothermal conditions, and laminar flow. By integrating the Yatta lava flow dimensions and the covered paleo-topography (slope angle) into the model, I was able to determine the pre-rift topography of the East African Plateau.
The modeling results yield a pre-rift slope of at least 0.2°, suggesting that the lava flow must have originated at a minimum elevation of 1,400 m. Hence, high topography in the region of the present-day Kenya Rift must have existed by at least 13.5 Ma. This inferred mid-Miocene uplift coincides with the two-step expansion of grasslands, as well as important radiation and speciation events in tropical Africa.
Accordingly, the combination of my results regarding the Yatta lava flow emplacement history, its location, and its morphologic character, validates it as a suitable “paleo-tiltmeter” and has thus to be considered as an important topographic and volcanic feature for the topographic evolution in East Africa.<br>Das Ostafrikanische Plateau ist ein eindrucksvolles Beispiel für aktive, kontinentale Grabenbildung, aber auch für geodynamische Hochebenenbildung mit weitreichendem klimatischen Einfluss auf die gesamte Region. Als integraler Bestandteil des Ostafrikanischen Grabensystems beläuft sich die mittlere Höhe des Plateaus auf durchschnittlich 1000 m ü.NN. Seine Lage korreliert gut mit der Präsenz einer halbkreisförmigen negativen Bouguer-Schwereanomalie, die an den Aufstieg eines Manteldiapirs im Untergrund gekoppelt ist. Dieser prägte die känozoische Krustenentwicklung seit seinem Aufstieg im Eozän-Oligozän.
Die Hebungsgeschichte und topographische Entwicklung des Hochlandes steht seither in enger Beziehung zum einsetzenden Vulkanismus, der Bildung erster Abschiebungssysteme und führte schließlich zur Entwicklung des heutigen Vollgrabensystems. Neueste Hypothesen lassen den Schluss zu, dass topographische Veränderungen als dominierende Einflussgrößen atmosphärischer Zirkulationsmuster sowie der regionalen Niederschlagsverbreitung anzusehen sind. Zusätzlich werden diese Prozesse durch die äquatoriale Lage des Ostafrikanischen Plateaus verstärkt und die Hebung dieser Region oft mit wichtigen Klima- und Umweltveränderungen in Ostafrika und angrenzende Gebiete in Verbindung gebracht. Während der weitreichende klimatische Einfluss des Hochlandes größtenteils akzeptiert ist, sind Zeitpunkt und Ausmaß seiner Heraushebung nicht eindeutig bestimmt und daher noch immer Grundlage bestehender Diskussionen. Diese Zwangslage hat ihre Ursache im Fehlen aussagekräftiger und datierbarer Referenzhorizonte.
Um den Hebungsbetrag zu quantifizieren und Beweise signifikanten Reliefs vor der Entwicklung des Grabensystems entlang des Ostafrikanischen Hochlandes zu erbringen, analysierte und modellierte ich einen der längsten terrestrischen Lavaströme. Dieser vor 13,5 Ma abgelagerte Yatta-Lavastrom hat mit 300 km Länge seinen Ursprung in der Region der heutigen östlichen Grabenschulter des zentralen Kenia-Rifts. Die phonolitische Lava ergoss sich entlang eines Flussbettes, das einst die östliche Flanke des Hochlandes entwässerte. Aufgrund unterschiedlicher Erosionspotentiale bildet der Lavastrom gegenwärtig ein positives Relief und befindet sich oberhalb des Athi Flusses, der parallel zum Paläofluß, und somit versetzt zu seinen früheren Verlauf, strömt.
Mein Ansatz der Lavastrom-Modellierung basiert auf einer Methode, die das Fließverhalten einer beliebigen Lava in Abhängigkeit von Temperatur und Magmenzusammensetzung in einem rechtwinkligen Kanal berechnet. Die wesentlichen Wachstumsmuster des Lavastroms sind durch ein eindimensionales Modell beschrieben, wobei Newtonsches Fließverhalten im Innern hinter der Lavastromfront von der zeitlichen Entwicklung der Viskosität und/oder der Fließgeschwindigkeit bestimmt wird. Vergleiche meiner Resultate mit verschiedenen Magmenzusammensetzungen zeigen, dass sich lange, kanalisierte Lavaströme mit hohen Ergussraten und schneller Platznahme bilden können. Dies geschieht unter annähernd isothermalen Bedingungen und erfordert laminares Fließen. Die Integration der Yatta- Lavastrom-Dimensionen und der bedeckten Paläotopographie (Neigungswinkel) in das Modell, erlaubte es mir die Topographie des Ostafrikanischen Hochlandes vor der Grabenbildung zu modellieren.
Das Ergebnis der Modellierung ergibt einen Neigungswinkel von mindestens 0,2° und impliziert, dass der Lavastrom seinen Ursprung in einer Höhe von mindestens 1400 m ü.NN gehabt haben muss. Somit existierte bereits vor 13,5 Ma hohe Topographie in der heutigen Region des zentralen Kenia-Rifts. Diese abgeleitete regionale Hebungsgeschichte im mittleren Miozän korreliert mit der zweistufigen Ausbreitung der Graslandschaften, sowie dem Aufkommen neuer Arten im tropischen Afrika.
Die Kombination aus Fließverhalten, Entstehungsort und morphologischer Eigenschaften macht den Yatta-Lavastrom zu einem “Paläoneigungsmesser” und wichtigen vulkanischen Untersuchungsobjekt für die topographische Entwicklung in Ostafrika.
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Milne, Fraser Dalton. "Topographic and material controls on the Scottish debris flow geohazard." Thesis, University of Dundee, 2008. https://discovery.dundee.ac.uk/en/studentTheses/eb4a6b03-8024-4818-8e92-ce1fd3c77209.
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Debris flows can be considered the most significant geological hazard in areas of high relief in Scotland having impacted upon slope foot infrastructure several times in recent years. The potency of this geohazard is anticipated to increase over the coming decades due to a climatologically enforced upturn in debris flow frequency. In thisresearch material and topographic controls on debris flow activity are investigated using a combination of field and laboratory based analysis of debris flows at six study sites across upland Scotland. Centrifuge modelling is also used to simulate theinitiation of debris flows in soils with varying particle size distributions.Spatial densities of debris flow measured in the field indicate that hillslopes underlain by sandstone and granitic bedrocks, which tend to be mantled by coarser sand rich soils, have a greater frequency of flows than those underlain by schist andextrusive lava bedrocks. Higher debris flow densities on slopes underlain by sandstone and granite lithologies are facilitated by high permeability in overlying regolith matrixes allowing more rapid increase in pore water pressures duringrainstorms although this is likely to be further influenced by packing and organic content. Centrifuge modelling of hillslope debris flows also demonstrate that sandier soils are generally geotechnically more susceptible to slope failure.The susceptibility of a hillslope to debris flow is strongly influenced by slope geometry and morphology. Hillslopes with persistently steep slopes and a high incidence of concavities, gullies and couloirs are topographically more predisposed todebris flow activity due to greater shear stresses and morphologically controlled, gravity induced concentrations of hillslope hydrology. The majority of material in channelised debris flows is entrained during the gully propagation stage of the massmovement. Consequently, such events can be considered accumulative channelised debris flows. Longer and steeper gullies with greater sediment capacities are more likely to yield larger flow mass movements. Coupling between open hillslopes andbedrock gullies is shown to be an essential component for conceptualisation of the debris flow geohazard.Due to the role they play in amplifying debris flow magnitude, hazard management should be focussed around bedrock gullies and stream channels. Highesthazard rankings should be assigned to slope foot infrastructure in proximity to gullied stream channels with high sediment capacities and long, steep profiles conducive to large accumulative channelised debris flows. To avoid detrimental aesthetic impact, hazard management should be strongly geared towards utilisation of lower impactexposure reduction techniques and less visually intrusive engineering approaches such as increasing culvert capacity to accommodate debris flows. During realignment or the planning of future transport infrastructure, culverts with capacities significantly exceeding those required for purely hydrodynamic considerations should be placed straight on to stream channels avoiding proximal gully bends.
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Rizo, Steven R. "Quantifying the Effect of Topographic Slope on Lava Flow Thickness: A First Step to Improve Lava Flow Volume Estimation Methods." Scholar Commons, 2018. http://scholarcommons.usf.edu/etd/7222.
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The volume of lava flows provide important information on the magnitude of volcanic eruptions, and accurate volumes are necessary to produce reliable models of lava flow emplacement or constrain the internal structure of volcanoes. The most accurate lava flow volumes are obtainable when the topography before and after an eruption are both known, but information for the topography before lava flow emplacement is absent in non-historic lava flows. To calculate the volume of non-historic lava flows, this pre-emplacement topography needs to be reconstructed. Common methods for this include using inverse distance-weighted averages or global polynomial interpolation methods, but these can still underestimate the volume of the flow, and the surface of the flow itself is not considered in these interpolations. A new calculation method seems necessary to better constrain the volume of lava flows, and including the lava flow surface in the volume calculation, given that it is generally excluded during interpolation of pre-emplacement topography, may be the solution to improving lava flow volume calculation for flows where the base surface is unknown. The 2012-2013 Tolbachik lava flow is used to look at potential relationships due to the availability of elevation data before and after the eruption. A quantitative analysis on the relationships between the slope of topography before and after lava flow emplacement and on the relationship between the slope and thickness of lava flows is performed. In addition to this, the slope of the topography calculated over local and regional scales is used as a new interpolation method, and the calculated thickness from the interpolated surface is compared to the known thickness for the lava flow.
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CUCCHIARO, SARA. "Assessing sediment dynamics and check dams efficiency in a debris-flow catchment using multi-temporal topographic surveys." Doctoral thesis, Università degli Studi di Trieste, 2019. http://hdl.handle.net/11368/2962385.
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Torrent control works have always been a fundamental tool for preventing torrential hazard in mountain catchments, where the sediment transport phenomena as debris flows are one of the most dangerous geomorphic processes affecting small steep basins. The linkages between sediment source areas on the hillslopes and channel network, along with the temporal and spatial distributions of channel storage, are key controls of debris-flow occurrence and magnitude. Consequently, the prevention of natural hazards related to debris-flows requires a better understanding of sediment dynamic. Among the hydraulic engineering structures, grade control dams and sediment retention dams are the most effective and common technique to manage debris flows and debris floods hazard. These structures could have important effects on sediment dynamic. Therefore, an integrated approach that analyses the debris-flow dynamic and its interactions with torrent control works, is needed to assess the efficiency of the realized structures and to improve the long-term hazard management at catchment scale. In spite of the widespread presence of such hydraulic structures in steep mountain streams worldwide, very little researches considered the role of check dams on sediment dynamics in debris-flow environments over time to enhance the planning of the torrent control works. The monitoring of debris-flow events, the estimation of debris-flow magnitude and frequency, and the analysis of spatial patterns in terms of eroded and deposited volumes, are fundamental to improve the sediment dynamic understanding. In the last two decades, High-Resolution Topography (HRT) has provided new opportunities to characterize debris-flow activity at different scales. Between these, the application of Structure from Motion (SfM) photogrammetry paired with Multi-View Stereo (MVS) algorithms has become a low-cost method to collect HRT at multiple temporal and spatial scales, also in rugged or inaccessible environments like those observed in debris-flow catchments. SfM allows carrying out HRT with high frequency; nevertheless, the SfM technique is limited at broad spatial scales. Therefore, other technologies as LiDAR surveys could be used to assess the sediment dynamic also at catchment scale. However, the use of HRT required the design of appropriate workflows for data post-processing and uncertainty assessment to compare multi-temporal surveys, especially in a topographically complex environment.
In this research, the effects of torrent control works on debris-flow dynamics were investigated by means of multi-temporal SfM and LiDAR surveys in the Moscardo torrent (eastern Italian Alps) where several check dams have been built over time. Methodological workflows enabled the realization of multi-temporal Digital Elevation Models (DEMs) which were compared (i.e., DoD) to quantify the debris mobilized and the time evolution of erosion and deposition patterns in debris-flow channels equipped with check dams. The DoDs data were integrated with a sediment connectivity analysis to have a whole assessment of debris-flow dynamic.
The results show that the check dams considerably modified debris-flow dynamics in the studied channel but their performance cannot be considered satisfactory. They temporary stored volumes of debris just after their construction, but soon when the structures were filled the check dams acted as sediment sources that increased debris-flow magnitude. Moreover, the sediment paths flowed around some check dams. These processes triggered the slope foot erosion and activated shallow landslides, further sediment source areas for debris-flow process. The analysis proposed in this work could help to improve design approaches and to obtain more realistic cost-benefit ratios of the adopted strategies and, in this way, select the best solutions.
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Nasser, Antoine-Alexis. "Advancing the representation of flows along topography in z-coordinate ocean models." Electronic Thesis or Diss., Sorbonne université, 2023. http://www.theses.fr/2023SORUS446.
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Les fonds marins exercent un contrôle majeur sur la circulation océanique. La représentation discrète de la topographie dans les modèles de circulation générale océanique (OGCM) géopotentiels crée des marches artificielles qui produisent des effets néfastes pour la simulation des courants. Cette thèse vise à établir des solutions adaptées pour résoudre les effets adverses des marches dans les OGCM. A partir de configurations idéalisées et en explorant le potentiel de la méthode de Pénalisation des Volumes de Brinkman (BVP), nous étudions la sensibilité des courants simulé aux frontières en marche d'escalier. Il est montré comment résoudre le 'spurious form drag' latéral (ou le 'staircase problem') mis en évidence par Adcroft et Marshall (1998). Les côtes (ainsi que les isobathes) représentées par des séries de marche deviennent lisses lorsqu'une condition miroir (glissement) est exactement appliquée sur l'écoulement à la côte. La formulation de la condition de glissement dans l'advection exprimé en 'flux-form' ou dans le tenseur visqueux symétrique produit dans le modèle du 'non-glissement' sur une topographie en marche d'escalier. Il est montré que la condition limite visqueuse doit changer le long des contours afin de simuler la rétroflexion du courants à un cape. Afin devenir insensible à la topographie en marche d'escalier, les modèles numériques devraient idéalement être physiquement convergés (c'est-à-dire que les caractéristiques principales de l'écoulement ne sont pas affectées par l'augmentation de la résolution spatiale en conservant les paramètres de viscosité et de friction constants). Il est montré que cette convergence peut être atteinte à une résolution plus faible en résolvant l'advection discrète des moments à l'aide de schémas utilisant un stencil élargi. On montre dans un overflow idéalisée l'impact de la résolution discrète de la quantité de mouvement sur la précision des écoulements le long des pentes en marche d'escalier. La méthode de BVP permet d'étaler l'interface terre-océan en définissant des cellules poreuses qui sont à moitié terre et à moitié océan. Étaler ainsi l'interface lisse les courants et réduit considérablement la diffusion numérique pendant la descente. Il est montré que la stabilité numérique de la méthode BVP peut être assurée en étalant suffisamment la frontière poreuse, et en ajustant de manière cohérente la perméabilité (friction dans les cellules poreuses). Les résultats soulignent le potentiel de la méthode BVP pour la meilleure représentation des courants le long des topographies dans les OGCM<br>The seafloor exerts a major control on ocean circulation. The discrete representation of marine topography in geopotential Ocean General Circulation Models (OGCMs) creates artificial steps that have adverse effects on the simulated circulation. This thesis aims at finding suitable ways to address the adverse effects of stepped topography in z-coordinate OGCMs. Using idealized configurations and exploring the potential of the Brinkman Volume Penalisation (BVP) method, we investigate the sensitivity of modelled currents to the presence of artificial steps along model boundaries. We first address the spurious lateral form drag (or textit{staircase problem}) highlighted by Adcroft and Marshall (1998). We show that staircase-like coastlines (and isobaths) behave as smooth boundaries when applying a textit{true} mirror condition on the boundary flow. The discrete implementation of free-slip using flux-form advection and a symmetric viscous stress tensor actually corresponds to no-slip along stepped topography. The choice of viscous boundary condition should vary with location to capture the retroflection of boundary currents at capes. To become insensitive to stepped topography, numerical models should ideally achieve physical convergence (i.e. the main characteristics of the flow are not affected by increasing spatial resolution while keeping viscous and frictional parameters constant). This convergence can be attained at lower resolution with a careful treatment of discrete momentum advection involving a large stencil. We highlight the impact of momentum advection schemes on the fidelity of simulated downslope currents within an idealised overflow configuration. The BVP method allows to spread the land-ocean interface, by introducing porous cells that are half-land half-ocean. We find that this spreading allows to smooth bottom currents and to reduce spurious mixing during downslope flow. The numerical stability of the BVP can be guaranteed by sufficient spreading of the boundary and by defining permeability (friction within porous cells) in a consistent way. The results underscore the potential of the BVP method to better represent flows along topography in OGCMs
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Raja, Keshav Jayakrishnan. "Internal waves and mean flow in the presence of topography." Thesis, Université Grenoble Alpes (ComUE), 2018. http://www.theses.fr/2018GREAU006/document.
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Les ondes internes jouent un rôle important dans de nombreux processus dans les océans.L’interaction entre les vagues internes et la topographie océanique a longtemps été un champ de recherche actif. Pourtant, il reste beaucoup de questions sur le sujet. Dans cette thèse, deux processus principaux sont examinés, à savoir la réflexion de faisceaux d’ondes internes sur une pente, et la génération d’ondes sous le vent sur un obstacle tridimensionnel, en utilisant des expériences de laboratoire et des simulations numériques.La réflexion non linéaire d’un faisceau d’onde interne sur une pente uniforme est étudiée à l’aide de la théorie des invisques bidimensionnels et de simulations numériques. Les interactions triadiques résonnantes entre les faisceaux d’ondes incidentes, réfléchies et de deuxième harmonique sont étudiées en développant la théorie existante et en les vérifiant avec des résultats pour des simulations numériques.Dans le cas de la réflexion de faisceaux d’ondes internes tridimensionnels, un fort flux horizontal moyen est induit par le faisceau d’onde, qui perturbe le champ d’onde et affaiblit les secondes harmoniques. La génération de ce flux moyen induit par les vagues est examinée à l’aide des résultats d’expériences et de simulations numériques tridimensionnelles. De plus,les effets de la rotation de fond sur le débit moyen induit par les vagues sont également étudiés à l’aide de simulations numériques.Le courant circumpolaire antarctique est considéré comme l’une des principales sources de mélange dans les océans. La modélisation en laboratoire du courant circumpolaire antarctique a été réalisée sur la plate-forme de Coriolis à LEGI pour étudier la traînée induite par la topographie sur le courant. L’expérience et ses résultats sont également présentés<br>Internal waves play an important role in many processes in oceans. The interaction be-tween internal waves and ocean topography has been an active field of research for long. Yetthere are many questions remaining on the topic. In this thesis, two main processes are ex-amined namely, the reflection of internal wave beams on a slope, and generation of lee wavesover a three-dimensional obstacle, using laboratory experiments and numerical simulations.The nonlinear reflection of an internal wave beam on a uniform slope is studied using two-dimensional inviscid theory and numerical simulations. The resonant triadic interactionsamong the incident, reflected and second harmonic wave beams are investigated developingon existing theory and verifying them with results for numerical simulations.In the case of reflection of three-dimensional internal wave beams, a strong mean horizon-tal flow is found to be induced by the wave beam, which perturbs the wave field and weakensthe second harmonics. The generation of this wave-induced mean flow is examined usingresults from experiments and three-dimensional numerical simulations. Furthermore, theeffects of background rotation on the wave induced mean flow are also studied using numer-ical simulations.The Antarctic Circumpolar Current is considered as one of the main sources of mixing inoceans. Laboratory modelling of the Antarctic Circumpolar Current was done in the Coriolisplatform at LEGI to study the topography induced drag on the current. The experiment andits results are also presented
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Skopovi, Ivan 1976. "The role of background flow variations in stratified flows over topography." Thesis, Massachusetts Institute of Technology, 2006. http://hdl.handle.net/1721.1/35632.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2006.<br>Includes bibliographical references (leaves 89-91).<br>As the atmosphere and oceans feature density variations with depth, the flow of a density-stratified fluid over topography is central to various geophysical and meteorological applications and has been studied extensively. For reasons of convenience and mathematical tractability, the majority of theoretical treatments of stratified flow over a finite-amplitude obstacle assume idealized background flow conditions, namely constant free-stream velocity and either a homogeneous or two-layer buoyancy-frequency profile. In this work, a numerical model is developed that accounts for general variations in the buoyancy-frequency profile far upstream and the presence of unsteadiness in the free-stream velocity. The model employs a second-order projection method for solving the Euler equations for stratified flow over locally confined topography in a horizontally and vertically unbounded domain - the flow configuration most pertinent to atmospheric applications - combined with absorbing viscous layers at the upper and lateral boundaries of the computational domain. Using this model, a study is first made of the effect of variations in the buoyancy frequency on the generation of mountain gravity waves.<br>(cont.) Balloon measurements reveal that, apart from a sharp increase (roughly by a factor of 2) at the so-called tropopause, atmospheric buoyancy-frequency profiles often feature appreciable oscillations (typical wavelength 1-2 kni). It is found that such short-scale oscillatory variations can have a profound effect on mountain waves owing to a resonance mechanism that comes into play at certain wind speeds depending on the oscillation length scale. A simple linear model assuming small sinusoidal buoyancy-frequency oscillations suggests, and numerical simulations for more realistic flow conditions confirm, that the induced gravity-wave activity under resonant conditions is significantly increased above and upstream of the mountain, causing transient wave breaking (overturning), similarly to resonant flow of finite depth over topography. The effect of temporal variations in the free-stream velocity is then explored for a range of amplitudes and periods typical of those encountered in the field. The simulations reveal that transient disturbances resulting from such variations can be significant, particularly in the nonlinear regime, and steady states predicted on the assumption of uniform wind may not be attainable.<br>by Ivan Skopovi.<br>Ph.D.
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Kiss, Andrew Elek, and Andrew Kiss@anu edu au. "Dynamics of laboratory models of the wind-driven ocean circulation." The Australian National University. Research School of Earth Sciences, 2001. http://thesis.anu.edu.au./public/adt-ANU20011018.115707.
Full textAbstract:
This thesis presents a numerical exploration of the dynamics governing
rotating flow driven by a surface stress in the " sliced cylinder " model
of Pedlosky & Greenspan (1967) and Beardsley (1969), and its close
relative, the " sliced cone " model introduced by Griffiths & Veronis
(1997). The sliced cylinder model simulates the barotropic wind-driven
circulation in a circular basin with vertical sidewalls, using a depth
gradient to mimic the effects of a gradient in Coriolis parameter. In the
sliced cone the vertical sidewalls are replaced by an azimuthally uniform
slope around the perimeter of the basin to simulate a continental slope.
Since these models can be implemented in the laboratory, their dynamics
can be explored by a complementary interplay of analysis and numerical
and laboratory experiments. ¶
In this thesis a derivation is presented of a generalised
quasigeostrophic formulation which is valid for linear and moderately
nonlinear barotropic flows over large-amplitude topography on an f-plane,
yet retains the simplicity and conservation properties of the standard
quasigeostrophic vorticity equation (which is valid only for small depth
variations). This formulation is implemented in a numerical model based
on a code developed by Page (1982) and Becker & Page (1990). ¶
The accuracy of the formulation and its implementation are confirmed by
detailed comparisons with the laboratory sliced cylinder and sliced cone
results of Griffiths (Griffiths & Kiss, 1999) and Griffiths & Veronis
(1997), respectively. The numerical model is then used to provide insight
into the dynamics responsible for the observed laboratory flows. In the
linear limit the numerical model reveals shortcomings in the sliced cone
analysis by Griffiths & Veronis (1998) in the region where the slope and
interior join, and shows that the potential vorticity is dissipated in an
extended region at the bottom of the slope rather than a localised region
at the east as suggested by Griffiths & Veronis (1997, 1998). Welander's
thermal analogy (Welander, 1968) is used to explain the linear
circulation pattern, and demonstrates that the broadly distributed
potential vorticity dissipation is due to the closure of geostrophic
contours in this geometry. ¶
The numerical results also provide insight into features of the flow at
finite Rossby number. It is demonstrated that separation of the western
boundary current in the sliced cylinder is closely associated with a
" crisis " due to excessive potential vorticity dissipation in the viscous
sublayer, rather than insufficient dissipation in the outer western
boundary current as suggested by Holland & Lin (1975) and Pedlosky
(1987). The stability boundaries in both models are refined using the
numerical results, clarifying in particular the way in which the western
boundary current instability in the sliced cone disappears at large
Rossby and/or Ekman number. A flow regime is also revealed in the sliced
cylinder in which the boundary current separates without reversed flow,
consistent with the potential vorticity " crisis " mechanism. In addition
the location of the stability boundary is determined as a function of the
aspect ratio of the sliced cylinder, which demonstrates that the flow is
stabilised in narrow basins such as those used by Beardsley (1969, 1972,
1973) and Becker & Page (1990) relative to the much wider basin used by
Griffiths & Kiss (1999). ¶
Laboratory studies of the sliced cone by Griffiths & Veronis (1997)
showed that the flow became unstable only under anticyclonic forcing. It
is shown in this thesis that the contrast between flow under cyclonic and
anticyclonic forcing is due to the combined effects of the relative
vorticity and topography in determining the shape of the potential
vorticity contours. The vorticity at the bottom of the sidewall smooths
out the potential vorticity contours under cyclonic forcing, but distorts
them into highly contorted shapes under anticyclonic forcing. In
addition, the flow is dominated by inertial boundary layers under
cyclonic forcing and by standing Rossby waves under anticyclonic forcing
due to the differing flow direction relative to the direction of Rossby
wave phase propagation. The changes to the potential vorticity structure
under strong cyclonic forcing reduce the potential vorticity changes
experienced by fluid columns, and the flow approaches a steady free
inertial circulation. In contrast, the complexity of the flow structure
under anticyclonic forcing results in strong potential vorticity changes
and also leads to barotropic instability under strong forcing. ¶
The numerical results indicate that the instabilities in both models
arise through supercritical Hopf bifurcations. The two types of
instability observed by Griffiths & Veronis (1997) in the sliced cone are
shown to be related to the western boundary current instability and
" interior instability " identified by Meacham & Berloff (1997). The
western boundary current instability is trapped at the western side of
the interior because its northward phase speed exceeds that of the
fastest interior Rossby wave with the same meridional wavenumber, as
discussed by Ierley & Young (1991). ¶
Numerical experiments with different lateral boundary conditions are also
undertaken. These show that the flow in the sliced cylinder is
dramatically altered when the free-slip boundary condition is used
instead of the no-slip condition, as expected from the work of Blandford
(1971). There is no separated jet, because the flow cannot experience a
potential vorticity " crisis " with this boundary condition, so the western
boundary current overshoots and enters the interior from the east. In
contrast, the flow in the sliced cone is identical whether no-slip,
free-slip or super-slip boundary conditions are applied to the horizontal
flow at the top of the sloping sidewall, except in the immediate vicinity
of this region. This insensitivity results from the extremely strong
topographic steering near the edge of the basin due to the vanishing
depth, which demands a balance between wind forcing and Ekman pumping on
the upper slope, regardless of the lateral boundary condition. The
sensitivity to the lateral boundary condition is related to the
importance of lateral friction in the global vorticity balance. The
integrated vorticity must vanish under the no-slip condition, so in the
sliced cylinder the overall vorticity budget is dominated by lateral
viscosity and Ekman friction is negligible. Under the free-slip condition
the Ekman friction assumes a dominant role in the dissipation, leading to
a dramatic change in the flow structure. In contrast, the much larger
depth variation in the sliced cone leads to a global vorticity balance in
which Ekman friction is always dominant, regardless of the boundary
condition.
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Thompson, LuAnne. "Flow over finite isolated topography." Thesis, Woods Hole, Mass. : Woods Hole Oceanographic Institution, 1990. http://catalog.hathitrust.org/api/volumes/oclc/23822687.html.
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Mengesha, Yoseph Gebrekidan. "Atmospheric boundary-layer flow over topography data analysis and representations of topography /." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp01/MQ39212.pdf.
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Hughes, Christopher William. "The effect of topography on ocean flow." Thesis, University of Oxford, 1992. http://ora.ox.ac.uk/objects/uuid:37b3f6b2-ce5f-45b3-b2ed-3325518b06bb.
Full textAbstract:
The rôle which topography plays in constraining ocean flow is investigated in several ways, mostly aimed at application to the Southern Ocean where topography is known to be important. The physics of topographic Rossby waves is discussed in some depth and a description of ocean flow in terms of a sum of topographic normal modes is developed. It is shown that the apparent incompleteness of topographic modes can often be circumvented by including a function which absorbs the nett input of potential vorticity. Some subtle problems with this description are dealt with, and a calculation of topographic modes for the Southern Ocean is presented, which shows that the modes are very localised, making the use of them to describe basin-wide flows difficult. The effect of interactions between stratification and topography is investigated in terms of a quasi-two-dimensional model which deals only with the depth-integrated flow, and the assumptions which go into the model are examined in detail both analytically and by calculating terms of interest from a data set produced by the Fine Resolution Antarctic Model. It is shown that advection of density in the Southern Ocean can be described to a first approximation as being due to a barotropic current with no vertical velocity, the horizontal component of the baroclinic flow producing very little effect. The balance of terms reveals interesting features in the modelled flow in the Southern Ocean, showing the value of this type of analysis. Finally, insight developed in the course of the investigation allows a simple model to be constructed representing the feedback between density advection and forcing due to density gradients. This model is used to provide an explanation for the fact that the FRAM model spins up linearly, where most simple models would predict a component of quadratic behaviour in the spin-up.
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Baldwin, Duncan Johnathan. "Boundary layer flow over three dimensional topography." Thesis, University of Southampton, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.307078.
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Tudball, Morgan J. "Electrified thin-film flow over inclined topography." Thesis, Loughborough University, 2018. https://dspace.lboro.ac.uk/2134/36253.
Full textAbstract:
We consider both a long-wave model and a first-order weighted-residual integral boundary layer (WIBL) model in the investigation of thin film flow down a topographical incline whilst under the effects of a normal electric field. The liquid is assumed to be a perfect dielectric, although is trivially extended to the case of a perfect conductor. The perfect dielectric case with no topography includes a simple modified electric Weber number which incorporates the relative electrical permittivity constant into itself. Linear stability analysis is carried out for both models, and critical Reynolds numbers which depend on the electric Weber number and the capillary number are produced. Regions of stability, convective instability and absolute instability are then determined for both models in terms of our electric Weber number and Reynolds number parameters in the case of no topography. Time-dependent simulations are produced to corroborate the aforementioned regions and investigate the effect of normal electric field strength in addition to sinusoidal and rectangular topographical amplitude on our system for various domain sizes. For the time-dependent simulations we find strong agreement with the linear stability analysis, and the results suggest that the inclusion of a normal electric field may have some stabilising properties in the long-wave model which are absent in the case of a flat wall, for which the electric field is always linearly destabilising. This stabilising effect is not observed for the same parameters in the WIBL model with a sinusoidal wall, although a similar effect is noticed in the WIBL model with a rectangular wall. We also investigate the simultaneous effect of domain size, wall amplitude and electric field strength on the critical Reynolds numbers for both models, and find that increasing the electric field strength can make large-amplitude sinusoidal topography stabilising rather than destabilising for the long-wave model. Continuation curves of steady solutions and bifurcation diagrams are also produced, and comparisons between the two models are made for various parameter values, which show excellent agreement with the literature. Subharmonic branches and time-periodic solutions are additionally included, similarly showing very good agreement with the literature.
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Holmes, Damian J. "Gravity waves in uniform windflow over topography." Thesis, University of Surrey, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.336449.
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Gaberšek, Saša. "The dynamics of gap flow over idealized topography /." Thesis, Connect to this title online; UW restricted, 2002. http://hdl.handle.net/1773/10098.
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Veremieiev, Sergii. "Gravity-driven continuous thin film flow over topography." Thesis, University of Leeds, 2011. http://etheses.whiterose.ac.uk/1688/.
Full textAbstract:
This thesis is directed primarily at a systematic theoretical investigation of gravity-driven thin film flow over various topographical features, the effect of inertia being of particular interest. The problem is solved using a hierarchy of models based, in order of decreasing complexity, on (i) the full Navier-Stokes system of equations; (ii) a depth averaged form of the latter; (iii) the lubrication equations. Every effort has been made to solve the underlying discrete equation set in each case efficiently using state-of-the-art solution strategies, thus guaranteeing accurate and mesh-independent predictions. The solution of models (ii) and (iii) centres on the use of a multigrid methodology together with automatic, error controlled, time-stepping and the proper treatment of any associated nonlinear advective terms. A discrete analogue of model (i), for both two- and three-dimensional flows, is obtained using a finite element formulation with the free surface parametrised via the method of spines and the system solved using a parallel multifrontal method together with a memoryefficient out-of-core storage approach. A comprehensive set of results is presented for flow over both one- and twodimensional topography, generated using models (ii) and (iii); the predictions obtained are contrasted with each other and compared with existing related experimental data. The free-surface disturbance arising for the problems investigated is revealed to be influenced significantly by the presence of inertia which leads to an increase in the magnitude and severity of the resulting capillary ridge, surge and trough formations present. A complementary exploration, using model (i) is undertaken which reveals the attendant internal flow structure. It shows that two-dimensional flow over spanwise topography and three-dimensional flow over localised trench topography can lead to different internal, inertia dependent, flow topologies; findings that are consistent with previously reported results for the well-known lid-driven cavity problem. Finally, the effect of a normal electric field on the free-surface disturbance generated by inertial thin film flow over topography is investigated using model (ii) coupled with a Fourier series separable solution of Laplace’s equation for the electric potential. Results for both two- and three-dimensional flow reveal that a significant electric field strength can be used to effectively planarise the free-surface capillary ridges and depressions that arise. The two-dimensional solutions obtained are consistent with those reported elsewhere for the case when inertia is neglected and highlight the importance attached to choosing an appropriate means of embodying the latter. Furthermore, the novel results generated for three-dimensional flow demonstrate that as Reynolds number increases, larger electric field strengths are required to planarise the associated free-surface disturbance.
20
Risch, Stephan Hermann. "Large-scale wave interactions in baroclinic flow with topography." Thesis, University of Oxford, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.312449.
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Draghicescu, Anca. "The influence of bed topography on ice sheet flow." Thesis, University of East Anglia, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.365045.
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McVicar, Alistair J. "Numerical simulations of flow-topography interaction using unstructured grids." Thesis, Imperial College London, 2012. http://hdl.handle.net/10044/1/10014.
Full textAbstract:
Eddies and jets are important components of global ocean momentum and heat budgets but are typically unresolved in low resolution global climate models. Herein, they are evaluated with an idealised model set–up that incorporates barotropic flow, past a cylinder on a β –plane. The flow dynamics are a function of two non–dimensional numbers: the Reynolds number and the [Symbol appears here. To view, please open pdf attachment] –parameter. The model used, Fluidity–ICOM, utilises unstructured meshes and a new stable mixed discontinuous/continuous finite element pair (P1DGP2). Unstructured meshes decrease the computational cost; the simulations using a non–uniform unstructured mesh had approximately 40% fewer nodes and ran at twice the speed of a uniform structured mesh for a comparable drag coefficient (Cd). The validation of Fluidity–ICOM was performed for a range of Reynolds numbers (0:0 < Re [Mathematical symbol appears here. To view, please open pdf attachment] 3 x 10[to the power of six]) and the percentage difference between published and Fluidity–ICOM values of Cd was found to be less than 10% for the regimes where the dynamics are essentially two–dimensional. The validation highlighted two important considerations: the position of the lateral domain boundary and the boundary mesh resolution. The wake structure for a moderate Reynolds number (1000) and [Symbol appears here. To view, please open pdf attachment] –parameter (75) changed significantly between coarse and fine boundary resolutions. The former was comprised of a double jet structure and the latter a single jet in the lee of the cylinder. This study demonstrated that resolving the frictional boundary layer dynamics is crucially important, as they substantially impact on the downstream flow. Evaluation of the single jet structure for a large parameter space [Mathematical formula appears here. To view, please open pdf attachment] revealed the presence of interfacial Rossby waves with both eastward and westward propagation with respect to the mean flow. The Rossby wave occurred due to the presence of a strong staircase gradient in absolute vorticity. As the Reynolds number increased for a fixed [Symbol appears here. To view, please open pdf attachment] –parameter, the presence of a stronger shear resulted in a faster phase speed of the Rossby wave and a stronger mean–flow. This parameter–space also showed a large dependence on drag to the [Symbol appears here. To view, please open pdf attachment] –parameter. Overall, this study has implications for the Gulf Stream separation and for understanding the interaction of the Antarctic Circumpolar Current (ACC) with topography.
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Brown, Harmony Rose. "Numerical simulations of stratified fluid flow over topography near resonance." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 2008. http://wwwlib.umi.com/cr/ucsd/fullcit?p1450159.
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Thesis (M.S.)--University of California, San Diego, 2008.<br>Title from first page of PDF file (viewed Mar. 25, 2008). Available via ProQuest Digital Dissertations. Includes bibliographical references (p. 83-85).
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Oikonomou, Emmanouil Konstantiou. "Stationary phase internal waves generated by flow along sloping topography." Thesis, University of Southampton, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.242690.
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Davis, Kevin S. (Kevin Scott) 1975. "Flow of nonuniformly stratified fluid of large depth over topography." Thesis, Massachusetts Institute of Technology, 1999. http://hdl.handle.net/1721.1/9409.
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Abdalla, Ayad A. "Bilayer channel and free-surface thin film flow over topography." Thesis, University of Leeds, 2014. http://etheses.whiterose.ac.uk/8819/.
Full textAbstract:
The work presented in this thesis focuses on gravity driven bilayer flow over a functional surface containing topography, with both liquids taken to be perfectly immiscible. Two such problems are considered and investigated systematically: (i) when the flow is confined between two rigid surfaces ("channel flow"); (ii) for the case of free-surface film flow down an inclined plane ("free-surface flow"). Both problems are underpinned by rigorous and comprehensive mathematical derivations, and the governing equation sets, resulting from application of the long-wave approximation, solved numerically using efficient and accurate finite difference algorithms programmed in C++. Such problems have received scant attention to-date. The channel flow work begins by revisiting the problem investigated by Lenz and Kumar (2007) and Zhou and Kumar (2012), to explore bilayer flow for the particular case of one Newtonian liquid lying above another and confined by rigid surfaces aligned parallel to each other, the lower one containing a steep-sided topographical feature. The investigation carried out serves a number of important purposes, the first being to establish the validity of the modelling and numerical approaches adopted, with the mesh independent results obtained found to be in excellent agreement with earlier work. In addition, the depth-averaged equation set derived in the thesis enables solutions to be obtained when the Reynolds number is non-zero, in contrast to the work of others which achieved only partial success. Finally, the situation when the upper wall of the channel is allowed to move horizontally with a constant speed, inducing a shear flow, is investigated for the first time. Bilayer free surface film flow over steep-sided topography, solutions to which have not been reported in the literature hitherto, is similarly investigated; comparisons having to be drawn for consistency and verification purposes with the case of single layer flow, Decré and Baret (2003), Gaskell et al. (2004), Veremieiev et al. (2010). Both zero and non-zero Reynolds number flow are considered and the governing equation sets and finite difference expressions re-derived to accommodate non-Newtonian behaviour, for the particular case of power-law liquids; it is found that for the latter case the associated depth-averaged equation set as formulated cannot be solved unless additional simplifications are adopted. In addition, for the case of Newtonian liquids, it is shown that the work can be extended to embody the more practical situation of three-dimensional bilayer film flow over topography. The mathematical model for this same film flow problem is extended to accommodate N layers, for the case when the Reynolds number is zero, with the derivation provided for completeness.
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Sinha, Bablu. "The influence of mesoscale eddies and topography on southern ocean flow." Thesis, University of Southampton, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.239650.
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Vo, Johnathan Hiep. "Modeling flow encountering abrupt topography using hybridizable discontinuous Galerkin projection methods." Thesis, Massachusetts Institute of Technology, 2017. http://hdl.handle.net/1721.1/113970.
Full textAbstract:
Thesis: S.M., Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2017.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (pages 85-89).<br>In this work novel high-order hybridizable discontinuous Galerkin (HDG) projection methods are further developed for ocean dynamics and geophysical fluid predictions. We investigate the effects of the HDG stabilization parameter for both the momentum equation as well as tracer diffusion. We also make a correction to our singularity treatment algorithm for nailing down a numerically consistent and unique solution to the pressure Poisson equation with homogeneous Neumann boundary conditions everywhere along the boundary. Extensive numerical results using physically realistic ocean flows are presented to verify the HDG projection methods, including the formation of internal wave beams over a shallow but abrupt seamount, the generation of internal solitary waves from stratified oscillatory flow over steep topography, and the circulation of bottom gravity currents down a slope. Additionally, we investigate the implementation of open boundary conditions for finite element methods and present results in the context of our ocean simulations. Through this work we present the hybridizable discontinuous Galerkin projection methods as a viable and competitive alternative for large-scale, realistic ocean modeling.<br>by Johnathan Hiep Vo.<br>S.M.
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Epifanio, Craig Charles. "High-drag states and lee vortices in stratified flow over topography /." Thesis, Connect to this title online; UW restricted, 1999. http://hdl.handle.net/1773/10072.
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Lu, Zhiming. "Numerical simulation of internal waves in stratified fluid flow over topography." Thesis, Loughborough University, 2004. https://dspace.lboro.ac.uk/2134/35028.
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The main purpose of this thesis is to investigate internal solitary wave generation and evolution in density-stratified fluid flows over both two-dimensional and three-dimensional bottom topographies using mainly numerical methods supported by some theoretical results. The numerical scheme to solve the forced KdV, KPII and KPI equation is a combination of the Runge–Kutta and Crank–Nicholson methods; a pseudo-spectral method is used to solve the two-dimensional fully nonlinear Euler equations in the streamfunction-vorticity form. The numerical results for a stratified flow over a two-dimensional step or an obstacle show that, in the resonant region, a forward step mainly generates upstream-advancing waves, while a backward step mainly generates downstream-propagating waves (a depression followed by lee waves), so the waves generated by a localised positive obstacle can be regarded as a simple superposition of the waves generated by its fore part and aft part. In contrast, the waves generated by a negative obstacle are quite different due to the nonlinear interaction between waves generated by its fore part and aft part.
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Carlin, Mattia. "The response of river bar topography to the hydrological flow regime." Doctoral thesis, Università degli studi di Trento, 2021. http://hdl.handle.net/11572/312573.
Full textAbstract:
Alternate bars are large-scale bedforms characterised by an ordered sequence of scour zones and depositional diagonal fronts alternating along channel banks, which are typical of straight channelized rivers. Due to their high relief and migration properties, they represent a problem in river management, because they affect navigation, increase the flooding risk and interact with instream structures. For this reason, in the last decades many studies took the challenge of defining suitable criteria able to describe their morphometric properties. Theoretical, experimental and numerical works have clearly demonstrated that bar occurrence is a threshold process governed by the width-to-depth ratio of the channel, β. If this parameter exceeds a critical threshold, βcr, an instability mechanism amplifies the riverbed perturbations occurring due to the effect of the turbulent flow on the cohesionless riverbed, leading to the spontaneous growth of finite amplitude bars. Under steady flow conditions, alternate bars achieve an equilibrium configuration, whose amplitude value is related to the difference β-βcr. Much less information is available to describe bar characteristics under variable flow conditions, when the width-to-depth ratio changes in time and the amplitude of bars evolves depending on the duration and the shape of the hydrograph. The effect of a single idealized flood on bar amplitude evolution was successfully described by the weakly nonlinear model of Tubino (1991), which was able to capture the trajectory of bar amplitude during different stages of the flood. Supported by experimental results, he found that the response of bars crucially depends on the ratio between the flood duration and the bar-growth timescale. Nevertheless, the effect of a complex flow regime, characterised by a sequence of flow events, is to a large extent unexplored. Specifically, (i) the definition of a criterion to predict the average response of alternate bars in a river reach subject to an hydrological flow regime and (ii) the quantification of bar amplitude evolution due to a complex flow regime are still to a large extent unexplored. The goals of this work are: (i) to investigate the dependence of bar properties to variable discharge conditions; (ii) to analyse the effect of flow unsteadiness in terms of duration and sequencing of flood events and derive the main hydrological characteristics that primarily control the average response of bar amplitude; (iii) to determine the long-term bar geometry and define the "bar-forming'' discharge, which is the theoretical discharge that if maintained indefinitely would produce the same long-term bar response as the natural hydrograph; (iv) to analyse the effect that a sequence of flood events composing a complex flow series has on the evolution of bar amplitude. To pursue these purposes, we adopted a methodology primary based on theoretical models, then supported and validated through the analysis of laboratory experiments and field data. The methodology and the key results for the different parts of this thesis can be summarized as follows: 1. First, the response of bar topography to different flow stages has been investigated both theoretically and through the analysis of experimental data, observing the dependence of alternate bars to peculiar threshold conditions. The validity of weakly nonlinear model of Colombini et al. (1987), originally defined in the neighborhood of the critical condition βcr, has been extended taking into account the emersion of bars for low flows. 2. Subsequently, the average response of bars to idealized flow series has been analysed, exploring their dependence on the duration and sequencing of flood events. The probability density function has been found to be the essential hydrological information of the flow series required to determine the long-term response of bar amplitude, while the integral scale of flow sequence is a suitable metric to quantify the unsteadiness of a flow regime. 3. Then, an innovative approach has been introduced to define an occurrence criterion for alternate bars in straightened river reaches that accounts for the hydrological regime, and to determine the average bar state, with the corresponding "bar-forming'' discharge. The key novelty with respect to the classical methods adopted so far to predict the long-term equilibrium channel geometry is that in this case the morphodynamical work acted on river bars by relatively low-flow stages enhancing their formation can be reversed by high-flow stages that suppress them. Therefore, both the occurrence criterion and the average state are found from a balance between the cumulative effects of bar-forming and bar-suppressing events. 4. Finally, the weakly nonlinear model of Colombini et al. (1987), originally defined to predict the evolution of bars under steady flow conditions, has been extended to reproduce a natural flow series by considering the basic flow varying in time. This approach allows us to (i) statistically investigate the effect of flood magnitude and duration on the variations of bar amplitude and (ii) to simulate the morphological response of a river to alterations of the hydrological regime.The long-term analysis of bar amplitude, as such as its evolution subject to the hydrological flow regime, have been applied to four different study cases, each of them characterised by a distinctive average bar response: two reaches of the Alpine Rhine River, upstream and downstream the confluence of the River Ill (Switzerland), respectively, the Adige River near Trento (Italy) and the Isère River near Montmèlian (France). The theoretical model is able to capture both qualitatively and quantitatively the observed bed response. Specifically, it predicts the occurrence of high-relief bars for the upstream reach of the Alpine Rhine River and for the Isère River, while a plane configuration is predicted for the Adige River. Also the intermediate response of the downstream reach of the Alpine Rhine River is reproduced, showing a predominant flat bed morphology with sporadic low-relief bars.
32
Carlin, Mattia. "The response of river bar topography to the hydrological flow regime." Doctoral thesis, Università degli studi di Trento, 2021. http://hdl.handle.net/11572/312573.
Full textAbstract:
Alternate bars are large-scale bedforms characterised by an ordered sequence of scour zones and depositional diagonal fronts alternating along channel banks, which are typical of straight channelized rivers. Due to their high relief and migration properties, they represent a problem in river management, because they affect navigation, increase the flooding risk and interact with instream structures. For this reason, in the last decades many studies took the challenge of defining suitable criteria able to describe their morphometric properties.
Theoretical, experimental and numerical works have clearly demonstrated that bar occurrence is a threshold process governed by the width-to-depth ratio of the channel, β. If this parameter exceeds a critical threshold, βcr, an instability mechanism amplifies the riverbed perturbations occurring due to the effect of the turbulent flow on the cohesionless riverbed, leading to the spontaneous growth of finite amplitude bars. Under steady flow conditions, alternate bars achieve an equilibrium configuration, whose amplitude value is related to the difference β-βcr.
Much less information is available to describe bar characteristics under variable flow conditions, when the width-to-depth ratio changes in time and the amplitude of bars evolves depending on the duration and the shape of the hydrograph. The effect of a single idealized flood on bar amplitude evolution was successfully described by the weakly nonlinear model of Tubino (1991), which was able to capture the trajectory of bar amplitude during different stages of the flood. Supported by experimental results, he found that the response of bars crucially depends on the ratio between the flood duration and the bar-growth timescale. Nevertheless, the effect of a complex flow regime, characterised by a sequence of flow events, is to a large extent unexplored. Specifically, (i) the definition of a criterion to predict the average response of alternate bars in a river reach subject to an hydrological flow regime and (ii) the quantification of bar amplitude evolution due to a complex flow regime are still to a large extent unexplored.
The goals of this work are: (i) to investigate the dependence of bar properties to variable discharge conditions; (ii) to analyse the effect of flow unsteadiness in terms of duration and sequencing of flood events and derive the main hydrological characteristics that primarily control the average response of bar amplitude; (iii) to determine the long-term bar geometry and define the "bar-forming'' discharge, which is the theoretical discharge that if maintained indefinitely would produce the same long-term bar response as the natural hydrograph; (iv) to analyse the effect that a sequence of flood events composing a complex flow series has on the evolution of bar amplitude.
To pursue these purposes, we adopted a methodology primary based on theoretical models, then supported and validated through the analysis of laboratory experiments and field data. The methodology and the key results for the different parts of this thesis can be summarized as follows:
1. First, the response of bar topography to different flow stages has been investigated both theoretically and through the analysis of experimental data, observing the dependence of alternate bars to peculiar threshold conditions. The validity of weakly nonlinear model of Colombini et al. (1987), originally defined in the neighborhood of the critical condition βcr, has been extended taking into account the emersion of bars for low flows.
2. Subsequently, the average response of bars to idealized flow series has been analysed, exploring their dependence on the duration and sequencing of flood events. The probability density function has been found to be the essential hydrological information of the flow series required to determine the long-term response of bar amplitude, while the integral scale of flow sequence is a suitable metric to quantify the unsteadiness of a flow regime.
3. Then, an innovative approach has been introduced to define an occurrence criterion for alternate bars in straightened river reaches that accounts for the hydrological regime, and to determine the average bar state, with the corresponding "bar-forming'' discharge. The key novelty with respect to the classical methods adopted so far to predict the long-term equilibrium channel geometry is that in this case the morphodynamical work acted on river bars by relatively low-flow stages enhancing their formation can be reversed by high-flow stages that suppress them. Therefore, both the occurrence criterion and the average state are found from a balance between the cumulative effects of bar-forming and bar-suppressing events.
4. Finally, the weakly nonlinear model of Colombini et al. (1987), originally defined to predict the evolution of bars under steady flow conditions, has been extended to reproduce a natural flow series by considering the basic flow varying in time. This approach allows us to (i) statistically investigate the effect of flood magnitude and duration on the variations of bar amplitude and (ii) to simulate the morphological response of a river to alterations of the hydrological regime.
The long-term analysis of bar amplitude, as such as its evolution subject to the hydrological flow regime, have been applied to four different study cases, each of them characterised by a distinctive average bar response: two reaches of the Alpine Rhine River, upstream and downstream the confluence of the River Ill (Switzerland), respectively, the Adige River near Trento (Italy) and the Isère River near Montmèlian (France). The theoretical model is able to capture both qualitatively and quantitatively the observed bed response. Specifically, it predicts the occurrence of high-relief bars for the upstream reach of the Alpine Rhine River and for the Isère River, while a plane configuration is predicted for the Adige River. Also the intermediate response of the downstream reach of the Alpine Rhine River is reproduced, showing a predominant flat bed morphology with sporadic low-relief bars.
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Gessese, Alelign Fekade. "Algorithms for Bed Topography Reconstruction in Geophysical Flows." Thesis, University of Canterbury. Mechanical Engineering, 2013. http://hdl.handle.net/10092/8673.
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Bed topography identification in open channel and glacier flows is of paramount importance for the study of the respective flows. In the former, the knowledge of the channel bed topography is required for modelling the hydrodynamics of open channel flows, fluvial hydraulics, flood propagation, and river flow monitoring. Indeed, flow models based on the Shallow Water Approximation require prior information on the channel bed topography to accurately capture the flow features. While in the latter, usable bedrock topographic information is very important for glacier flow modellers to accurately predict the flow characteristics. Experimental techniques to infer the bed topography are usually used but are mostly time consuming, costly, and sometimes not possible due to geographical restrictions. However, the measurement of free surface elevation is relatively easy. Alternative to experimental techniques, it is therefore important to develop fast, easy-to-implement, and cost-effective numerical methods.
The inverse of the classical hydrodynamic problem corresponds to the determination of hydraulic parameters from measurable quantities. The forward problem uses model parameters to determine measurable quantities. New one-shot and direct pseudo-analytical and numerical approaches for reconstructing the channel bed topography from known free surface elevation data is developed for one-dimensional shallow water flows. It is shown in this work that instead of treating this inverse problem in the traditional partial differential equation (PDE)-constrained optimization framework, the governing equations of the direct problem can be conveniently rearranged to obtain an explicit PDE for the inverse problem. This leads to a direct solution of the inverse problem which is successfully tested on a range of benchmark problems and experimental data for noisy and noiseless free surface data. It was found that this solution approach creates very little amplification of noise.
A numerical technique which uses the measured free surface velocity to infer the channel bed topography is also developed. The one-dimensional shallow water equations along with an empirical relationship between the free surface and the depth averaged velocities are used for the inverse problem analysis. It is shown that after a series of algebraic manipulation and integration, the equation governing the inverse problem simplifies to a simple integral equation. The proposed method is tested on a range of analytical and experimental benchmark test cases and the results confirm that, it is possible to reconstruct the channel bed topography from a known free surface velocity distribution of one-dimensional open channel flows.
Following the analysis of the case of one-dimensional shallow water flows, a numerical technique for reconstructing the channel bed topography from known free surface elevation data for steep open channel flows is developed using a modified set of equations for which the zero-inertia shallow water approximation holds. In this context, the shallow water equations are modified by neglecting inertia terms while retaining the effects of the bed slope and friction terms. The governing equations are recast into a single first-order partial differential equation which describes the inverse problem. Interestingly, the analysis shows that the inverse problem does not require the knowledge of the bed roughness. The forward problem is solved using MacCormack’s explicit numerical scheme by considering unsteady modified shallow water equations. However, the inverse problem is solved using the method of characteristics. The results of the inverse and the forward problem are successfully tested against each other.
In the framework of full two-dimensional shallow water equations, an easy-to-implement and fast to solve direct numerical technique is developed to solve the inverse problem of shallow open channel flows. The main underlying idea is analogous to the idea implemented for the case of one-dimensional reconstruction. The technique described is a “one-shot technique” in the sense that the solution of the partial differential equation provides the solution to the inverse problem directly. The idea is tested on a set of artificial data obtained by first solving the forward problem.
Glaciers are very important as an indicator of future climate change or to trace past climate. They respond quickly compared to the Antarctica and Greenland ice sheets which make them ideal to predict climate changes. Glacier bedrock topography is an important parameter in glacier flow modelling to accurately capture its flow dynamics. Thus, a mathematical technique to infer this parameter from measured free surface data is invaluable. Analogous to the approaches implemented for open channel flows, easy-to-implement direct numerical and analytical algorithms are developed to infer the bedrock topography from the knowledge of the free surface elevation in one space dimension. The numerical and analytical methods are both based on the Shallow Ice Approximation and require the time series of the ablation/accumulation rate distribution. Moreover, the analytical method requires the knowledge of a non-zero glacier thickness at an arbitrary location. Numerical benchmark test cases are used to verify the suitability and applicability of the algorithms.
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Du, Jun. "Estimation de l'épaisseur des coulées de lave sur la Lune et le Mercure basée sur la modélisation de la dégradation topographique de cratères d’impact." Thesis, Université Côte d'Azur (ComUE), 2019. http://www.theses.fr/2019AZUR4099.
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Dans cette étude, les cratères partiellement enterrés dans la maria lunaire et dans les plaines lisses septentrionales de Mercure ont été identifiés à l'aide de données récemment acquises concernant l'optique, l'élévation et la composition, et les épaisseurs de coulées de lave proches des cratères partiellement enterrés ont été estimées par modélisation numérique de leur dégradation topographique. Au chapitre 1, je présente d'abord le contexte géologique des plaines volcaniques de la Lune et de Mercure. Ensuite, je vais résumer toutes les méthodes qui ont été utilisées pour estimer l’épaisseur des coulées de lave sur la Lune et Mercure, ainsi que les progrès de la recherche sur la dégradation topographique du cratère. Au chapitre 2, je présente les ensembles de données de télédétection utilisés dans cette étude. Ensuite, les critères utilisés pour identifier les cratères partiellement enterrés sont discutés. Une méthode d'estimation de l'épaisseur des coulées de lave est proposée ultérieurement, basée sur la dégradation topographique de cratères partiellement enterrés. L'épaisseur de coulée de lave la mieux adaptée a ensuite été déterminée en minimisant la différence entre le profil final modélisé et le profil observé. Au chapitre 3, afin de résoudre l'équation de diffusion topographique, le profil d'altitude d'un nouveau cratère d'impact est construit comme condition initiale. Pour les cratères d’impact frais lunaires, nous avons construit un ensemble de profils topographiques qui prennent en compte à la fois la taille des cratères et les types de cibles. Pour les nouveaux cratères d’impact sur Mercure, nous avons construit des profils topographiques qui incluent uniquement des cratères de transition et complexes. Comme décrit au chapitre 4, les épaisseurs de basalte ont été inversées en utilisant 41 cratères de maria dont les bords sont complètement exposés. Le résultat montre que les épaisseurs estimées en basalte mare varient de 33 à 455 m, avec une valeur médiane de 105 m. Nous avons ensuite calculé le volume total et le taux d'éruption des basaltes des maria lunaires et avons constaté que le taux estimé d'éruption des basaltes des maria atteignait un sommet de 3,4 Ga, puis diminuait avec le temps, indiquant un refroidissement progressif de l'intérieur de la lune. Nous avons également constaté que la diffusivité topographique des cratères lunaires augmente avec le diamètre et est presque invariante dans le temps. Au chapitre 5, je présente un résultat similaire pour Mercure. Les épaisseurs de coulées de lave ont été inversées pour 17 cratères dont les bords ont été exposés et enduits de plus de 50% de leur circonférence. Le résultat montre que les épaisseurs de coulées de lave varient de 7 à 419 m, avec une valeur médiane de 218 m. Nous avons ensuite calculé le volume total et le taux d’éruption des coulées de lave. En comparant la diffusivité topographique sur la Lune à celle sur Mercure, on peut constater que les deux valeurs sont similaires. Comme indiqué au chapitre 6, il reste quelques problèmes à résoudre à l'avenir. Tout d'abord, j'ai utilisé une géométrie axisymétrique simple lors de la résolution analytique de l'équation de diffusion topographique et n'ai pas envisagé un processus de dégradation topographique entièrement tridimensionnel. Deuxièmement, les diffusivités topographiques inversées présentent un large intervalle d’incertitude et ne sont pas bien contraintes. Troisièmement, les cratères complexes ont généralement un mécanisme de formation compliqué et un fond géologique et une morphologie de cratère variables, ce qui entraîne une variabilité et une incertitude considérables des relations morphométriques du cratère<br>In this study, partially buried craters on the lunar maria and the northern smooth plains of Mercury were identified using recently acquired optical, elevation, and composition data, and lava flow thicknesses near partially buried craters were estimated by numerically modeling their topographic degradation. In Chapter 1, I first introduce the geologic background of the volcanic plains on the Moon and Mercury. Next, I will summarize all the methods that have been used to estimate the lava flow thicknesses on the Moon and Mercury, as well as the research progress on the crater topographic degradation. In Chapter 2, I present the remote sensing datasets used in this study. Then, the criteria used to identify partially buried craters are discussed. A lava flow thickness estimation method is later proposed based on the topographic degradation of partially buried craters. The best fitting lava flow thickness was then determined by minimizing the difference between the modeled final profile and the observed profile. In Chapter 3, in order to solve the topographic diffusion equation, the elevation profile of a fresh impact crater is constructed as the initial condition. For lunar fresh impact craters, we constructed a set of topographic profiles that consider both crater sizes and target types. For fresh impact craters on Mercury, we constructed topographic profiles that only include transitional and complex craters. As described in Chapter 4, the basalt thicknesses were inverted using 41 mare craters whose rims are completely exposed. The result shows that the estimated mare basalt thicknesses vary from 33 to 455 m, with a median value of 105 m. We then calculated the total volume and eruption rate of lunar mare basalts, and found that the estimated eruption rate of mare basalts peaked at 3.4 Ga and then decreased with time, indicating a progressive cooling of the lunar interior. We also found that the topographic diffusivity of lunar craters increases with diameter and is almost invariant with time. In Chapter 5, I present a similar result for Mercury. The lava flow thicknesses were inverted for 17 craters whose rims were exposed and embayed for more than 50% of its circumference. The result shows that the lava flow thicknesses vary from 7 to 419 m, with a median value of 218 m. We then calculated the total volume and eruption rate of the lava flows. Comparing the topographic diffusivity on the Moon with that on Mercury, it can be found that both values are similar to each other. As shown in Chapter 6, there are some remaining issues that need to be solved in the future. First, I employed a simple axisymmetric geometry when analytically solving the topographic diffusion equation and did not consider a fully three-dimensional topographic degradation process. Second, the inverted topographic diffusivities have a large range of uncertainty and are not well constrained. Third, complex craters usually have complicated formation mechanism and a variable geologic background and crater morphology, resulting in considerable variability and uncertainty in the crater morphometric relations
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Bevan, Edward. "Chaotic advection in shallow flows over bed topography." Thesis, University of Oxford, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.437158.
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Söderberg, Stefan. "Trapped supercritical flows: Numerical simulations with idealized topography." Thesis, Uppsala universitet, Institutionen för geovetenskaper, 1999. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-392620.
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Numerical simulations of supercritical coastal flows have been performed. The meso-γ-scale model which has been used in this study is non-linear, hydrostatic and has a higher-order turbulence closure. Previous studies of supercritical coastal flows with this model have given rise to some questions and hypotheses, e. g. is the gradual curvature of the main coastal mountains north of Cape Mendocino sufficient to excite an expansion fan? Is the local terrain of Cape Mendocino responsible for the collapse of the marine atmospheric layer (MABL) in Shelter Cove? This study was designed to answer these questions. The terrain used in the simulations was generated by a simple analytical function and fitted to the real terrain north of Cape Mendocino in a sense that it would reflect it as good as possible, neglecting ”small” changes in the orientation of the coast and height of the terrain. This made it possible to test hypotheses related to the coastline shape one by one. Simulations that were performed are: Piecewise linear coasts with constant terrain height where the change in coastline orientation, the height of the inversion and strength of the background wind speed was varied; Piecewise linear coasts where the height of the terrain was varying along the coast; Curved coastlines with different curvatures; Piecewise linear coasts with simplified capes perpendicular to the coast where the height of the cape was varied. It was found that the angle with which the coast turns away from the flow regulates the amount of acceleration in the following expansion fan. A decreasing height of the terrain along the coast lead to an increased acceleration of the flow, the largest acceleration was found when the slope of the terrain was confined to the change in coastline orientation. It was concluded that this is comparable to an increased change in coastline orientation. The simulations with curved coastlines confirmed the hypothesis that the gradual curvature of the main coastal mountains north of Cape Mendocino is sufficient to excite an expansion fan. In fact, a curved coastline leads to a stronger acceleration of the flow than a piecewise linear coastline. One of the most striking features in this study was that the acceleration of the flow started far upstream of the change in coastline orientation, even though the flows were supercritical. This phenomenon was mainly found in the cases with the highest wind speeds. It is suggested that the upstream acceleration of the flow is due to either high amplitude gravity waves propagating within the MABL or internal gravity waves propagating above the inversion. When a cape was inserted perpendicular to the main coastline, this showed that even with a cape as low as approximately half the depth of the MABL, the flow was significantly blocked. Indications of wave-breaking on the lee side of the cape was also found, which confirmed the hypothesis that the local terrain of Cape Mendocino is responsible for the collapse of the MABL in Shelter Cove.
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Hakes, Kyle Jeffrey. "Tidally Generated Internal Waves from Asymmetric Topographies." BYU ScholarsArchive, 2020. https://scholarsarchive.byu.edu/etd/8717.
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Internal waves are generated in stratified fluids, like the ocean, where density increases with depth. Tides are one of the major generation mechanisms of internal waves. As the tides move water back and forth over underwater topography, internal waves can be generated. The shape of the topography plays a major part in the properties of the generated internal wave and the type of wave and energy is known for multiple symmetric topographies, such as Gaussian or sinusoidal. In order to further understand the effects topographic shape plays, the effect of asymmetry on internal waves is investigated. First, two experimental methods are compared to evaluate which will capture the relevant information for comparing waves generated from oscillating asymmetric topographies. Two experimental methods are often used in internal wave research, Synthetic Schlieren (SS) and Particle Image Velocimetry (PIV). Both SS and PIV experimental methods are used to analyze a set of experiments in a variety of density profiles and with a variety of topographies. The results from these experiments are then compared both qualitatively and quantitatively to decide which method to use for further research. In the setup, the larger field of view of SS results in superior resolution in wavenumber analysis, when compared to PIV. In addition, SS is 25% faster to setup and significantly cheaper. These are the deciding factors leading to the selection of SS as the preferred experimental method for further tests regarding tidally generated internal waves from asymmetric topographies. Previous experimental and theoretical research on tidally generated internal waves has most often used symmetric topographies. However, due to the complex nature of real ocean topography, the effect of asymmetry can not be overlooked. A few studies have shown that asymmetry can have a significant effect on internal wave generation, but topographic asymmetry has not been studied in a systematic manner up to this point. This work presents a comparison of tidally generated internal waves from nine different asymmetric topographies, consisting of a steeper Gaussian curve on one side, and a wider Gaussian curve on the other. The wider curve has varying amplitude from 1 to 0.6 of the steeper curve's amplitude, and two oscillation frequencies are explored. First, kinetic energy density in tidally generated internal waves is compared qualitatively and quantitatively, in both physical and Fourier space. When compared to similar symmetric topographies, the asymmetric topographies varied distinctly in the amount of internal wave kinetic energy generated. In general, internal wave kinetic energy generated from asymmetric topographies is higher for waves generated at a lower frequency than at a higher frequency. Also, kinetic energy is higher in internal waves on the relatively steeper side of the topography. There is very little kinetic energy in the higher wavenumbers, with most of the internal waves being generated at the lower wavenumbers. The amplitude does not make an appreciable difference in the wavenumber at which the internal waves are generated. Thus, the differences quantified here are due solely to changing slope, showing a significant impact of a relatively slight asymmetry.
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Petroliagis, Thomas I. "Studies of barotropic flow over topography using a Galerkin Finite Element model." Thesis, Monterey, California. Naval Postgraduate School, 1988. http://hdl.handle.net/10945/23411.
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A finite element shallow-water model is tested with two types of surface topography. The model uses rectangular subdivisions in a vorticity-divergence formulation, and a semi-implicit time discretization. In the first experiment an east-west ridge or valley is placed in a channel with east-west periodic conditions. Linear quasi-geostrophic solutions are derived with the rigid lid assumption. The Rossby waves are successfully simulated in the model with linear solutions as the initial conditions. The model phase speeds are very close to the analytic values when the latter are properly corrected. In the second experiment a ridge is placed across the channel and the Coriolis parameter is set to zero. The initial conditions consist of a uniform flow through the channel and constant free-surface height. The numerical simulations agree with hydraulic jump theory. In the jump cases the model predicts increasing wind speeds and decreasing free surface heights. Higher spatial resolution would be required to properly simulate the details of the hydraulic jump formation. (fr)
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ISNARD, ANDRE AUGUSTO. "COMPUTATIONAL INVESTIGATION ON THE FLOW AND ATMOSPHERIC POLLUTANT DISPERSION OVER COMPLEX TOPOGRAPHY." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2004. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=5174@1.
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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO<br>O objetivo principal do presente trabalho foi investigar
computacionalmente o escoamento e a dispersão de
poluentes atmosféricos sobre topografias complexas
tridimensionais em escala de laboratório. Foram
realizadas simulações numéricas de escoamentos neutros e
estavelmente estratificados sobre colinas e também sobre
terreno plano. A modelagem matemática, baseada na solução
das equações gerais de conservação, inclui o modelo de
tensões de Reynolds para a turbulência e um modelo de
duas camadas para o tratamento do escoamento na região
próxima à parede. O código comercial Fluent (Versão
6.0.12), que emprega o método de volumes finitos, foi
utilizado nas simulações computacionais. Os resultados
numéricos foram comparados a dados obtidos em
experimentos em túnel de vento disponíveis na literatura.
Também foram realizadas comparações com resultados
obtidos com a utilização do modelo (k menos épsilon)
clássico. A
comparação entre os resultados obtidos com as diversas
modelagens numéricas e os dados experimentais mostrou que
a utilização conjunta do modelo de tensões de Reynolds e
do tratamento em duas camadas produziu os melhores
resultados na predição do escoamento. O desempenho dessa
modelagem foi particularmente superior na representação
da recirculação no escoamento na região a jusante da
colina. Com relação ao cálculo das concentrações, os
resultados obtidos foram razoáveis nas regiões mais
distantes da fonte quando comparados aos experimentais.
Na região mais próxima à fonte emissora, foram calculadas
concentrações excessivamente altas ao nível do solo.
Estas discrepâncias foram atribuídas ao fato de ter-se
utilizado um modelo de difusividade turbulenta isotrópica
para os cálculos da dispersão turbulenta do poluente.
Ainda assim, os campos de concentrações apresentados
mostraram importantes aspectos qualitativos relativos ao
problema como, por exemplo, os efeitos da estabilidade
atmosférica na dispersão do poluente, que foram
adequadamente previstos.<br>The main objective of the present work was to investigate
computationally the flow and the dispersion of atmospheric
pollutants over three dimensional complex topographies in
laboratory scale. The investigations included the numerical
simulation on the neutral and stably stratified flows over
hills and flat terrain. The mathematical model was based on
the solution of the general conservation equations and
included the Reynolds stress model for turbulence and a two
layer zonal model for the flow treatment in the near wall
region. The commercial code Fluent (Version 6.0.12), which
is based on the finite volume method, was employed in the
computational simulations. The numerical results were
compared to data obtained in wind tunnel experiments,
available in the literature. Comparisons were also made
with results obtained by employing the standard (k less
épsilon) model
for turbulence.
The comparisons between the experimental data and the
numerical results showed that the combined use of the
Reynolds stress model and the two layer treatment provided
the best results for the flow representation. This modeling
approach was particularly superior in representing the flow
recirculation on the leeside of the hill.
The predicted concentrations results were reasonably good
at regions far away from the emission source. In the near
source regions, the ground level concentrations were
overestimated by the numerical modeling. These
discrepancies were attributed to the employment of an
isotropic turbulent diffusivity model in the turbulent
dispersion calculations. Nevertheless, the calculated
concentration fields represented well important qualitative
features of PUC Rio.
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Lim, Kahn Yung 1976. "Trapped disturbances and effects of tropopause height in stratified flow over topography." Thesis, Massachusetts Institute of Technology, 2001. http://hdl.handle.net/1721.1/89314.
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Zhang, Xiaoyang. "Soil-erosion modelling at the global scale using remote sensing and GIS." Thesis, King's College London (University of London), 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.321948.
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Penserini, Brian. "Debris Flow Network Morphology and a New Erosion Rate Proxy for Steepland Basins with Application to the Oregon Coast Range and Cascadia Subduction Zone." Thesis, University of Oregon, 2015. http://hdl.handle.net/1794/19276.
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Reaches dominated by debris flow scour and incision tend to greatly influence landscape form in steepland basins. Debris flow networks, despite their ubiquity, have not been exploited to develop erosion rate proxies. To bridge this gap, I applied a proposed empirical function that describes the variation of valley slope with drainage area in fluvial and debris flow reaches of steepland channel networks in the Oregon Coast Range. I calibrated a relationship between profile concavity and erosion rate to map spatial patterns of long-term uplift rates assuming steady state. I also estimated the magnitude and inland extent of coseismic subsidence in my study area. My estimates agree with field measurements in the same area along the Cascadia margin, indicating that debris flow valley profiles can be used to make interpretations from spatial patterns of rock uplift that may better constrain physical models of crustal deformation.
This thesis includes unpublished co-authored material.
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Rump, Owen James. "Non-rotating and rotating free surface flows over topography." Thesis, University College London (University of London), 2007. http://discovery.ucl.ac.uk/1446071/.
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An important effect in atmosphere and ocean dynamics is the drag exerted by topography, in the form of mountain ranges and individual mountains, on incident flows. Because the scale of topographic variations are usually small compared to the resolution of global-scale numerical models, drag effects must often be parameterised. This thesis aims to understand topographic drag in highly idealised numerical models with a view to demonstrating where efforts in parameterisation may be best directed. Specifically, the thesis considers single-layer and one and one half layered flow (where a single layer lies below an infinitely deep layer of slightly lower density) over topography, inspired by a series of rotating tank experiments. The flow behaviour is strongly affected by the Proude number F of the flow - the ratio of the oncoming flow to the speed of long free gravity waves. The transcritical regime F 1, in which there is a close analogy with compressible gas dynamics, is investigated as a novel limit of the Shallow-Water Equations. Scaling laws for the drag are verified against numerical integrations and various flow regimes for rotating and non-rotating flows delineated. Supercritical flow {F > 1) is also investigated, focusing on both the drag and breaking waves in the far-field, which in the rotating case is shown to depend on a single parameter.
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Lindeman, John David. "A numerical study of topographical effects on flow regimes in the lower atmosphere." Fairfax, VA : George Mason University, 2008. http://hdl.handle.net/1920/3063.
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Thesis (Ph.D.)--George Mason University, 2008.<br>Vita: p. 138. Thesis director: Zafer Boybeyi. Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Computational Sciences and Informatics. Title from PDF t.p. (viewed July 3, 2008). Includes bibliographical references (p. 132-137). Also issued in print.
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Eberly, Lauren Elizabeth. "Internal Wave Generation Over Rough, Sloped Topography: An Experimental Study." BYU ScholarsArchive, 2012. https://scholarsarchive.byu.edu/etd/3437.
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Internal waves exist everywhere in stratified fluids - fluids whose density changes with depth. The two largest bodies of stratified fluid are the atmosphere and ocean. Internal waves are generated from a variety of mechanisms. One common mechanism is wind forcing over repeated sinusoidal topography, like a series of hills. When modeling these waves, linear theory has been employed due to its ease and low computational cost. However, recent research has shown that non-linear effects, such as boundary layer separation, may have a dramatic impact on wave generation. This research has consisted of experimentation on sloped, sinusoidal hills. As of yet, no experimental research has been done to characterize internal wave generation when repeated sinusoidal hills lie on a sloped surface such as a continental slope or a foothill. In order to perform this experiment, a laboratory was built which employed the synthetic schlieren method of wave visualization. Measurements were taken to find wind speed, boundary layer thickness, and density perturbation. From these data, an analysis was performed on wave propagation angle, wave amplitude, and pressure drag. The result of the analysis shows that when wind blows across a series of sloped sinusoidal hills, fluid becomes trapped in the troughs of the hills resulting in a lower apparent forcing amplitude. The generated waves contain less energy than linear predictions. Additionally, the sloped hills produce waves which propagate at an angle away from the viewer. A necessary correction, which shifts from the reference frame of the observer to the reference plane of the waves is described. When this correction is applied, it is shown that linear theory may only be applied for low Froude numbers. At high Froude numbers, the effect of the boundary layer is great enough that the wave characteristics deviate significantly from linear theory predictions. The analyzed data agrees well with previous studies which show a similar deviation from linear theory.
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Woodhead, David John. "Computation of air flow over steep and complex topography using terrain-intersecting meshes." Thesis, University of Leeds, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.496211.
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Cowling, Neil Peter. "Thin film flow over a topography and non-isothermal droplets : a numerical study." Thesis, University of Leeds, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.551241.
Full textAbstract:
Research towards understanding continuous thin film flows and droplet spreading is as relevant today as it ever was. Theoretically, lubrication theory has played a pivotal role with the equations involved requiring numerical solution. The most commonly employed solvers are based upon either a time-splitting or multigrid strategy; no consensus has been reached as to which is the most accurate and efficient. With modern engineering applications demanding solutions at smaller and smaller scales, in turn requiring the use of finer grids to ensure mesh independent solutions, efficiency is a necessary consideration. The work of this thesis divides into two strands. First, a three-dimensional continuous film problem is modelled and formulated in two equivalent ways: as two coupled second-order equations, or as a single fourth-order equation. These are solved numerically by multigrid and time-splitting solvers, finding that, due to the larger time-steps which are possible, the multigrid scheme, when solving the coupled equations, offers the fastest route to converged solutions; the accuracy of solution for each solver is comparable. Following the use of static mesh adaptivity, the conclusions drawn for uniform meshes concerning the solvers are found to be equally valid on non-uniform meshes. Following that, a new model is proposed to investigate unpinned droplets evaporating from a thick, heated substrate into the surrounding atmosphere. A study of accuracy and efficiency is also conducted for a droplet spreading problem; it isfound that the multigrid scheme, when solving the coupled system of equations, is again the most efficient solver. This scheme is adapted for the evaporation model, leading to excellent qualitative and some quantitative agreement with previous studies of both the pinned and unpinned stages of evaporation. To the' author's knowledge, this is the first model to successfully capture the behaviour in both stages of evaporation and also the change in this behaviour depending upon the properties of the substrate and liquid considered.
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Sridhar, Harshitha. "The Impact of Boundary Condition on Groundwater Flow : Topography v/s Recharge Controlled." Thesis, KTH, Hållbar utveckling, miljövetenskap och teknik, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-286148.
Full textAbstract:
Groundwater interactions at a regional scale are of great importance to characterize subsurface flow processes. Extensive researches have been conducted previously to determine the main factors controlling the regional implications on groundwater flux circulation. Groundwater circulation occurs due to variation in the groundwater table (hydraulic gradient) across the spatial scale. Previous research highlighted the correlation between groundwater table with both topography variation and the recharge from precipitation. This study aims to highlight the impact of these boundary conditions. Five catchments located across different regions of Sweden with different topographical, hydrological, and meteorological properties considered for this study: Bodalsån, Forsmarksån, Tullstorpsån, Sävaån, and Krycklan. Relevant data were collected and numerical models were set up in steady- state conditions for each of these catchments, using 3D Multiphysics COMSOL. Models were set up for both of the boundary conditions, using 10 m grid resolution.Groundwater flux profiles along the depth of the catchments were obtained as a result, in which significant differences were observed. This was associated predominantly with the difference in the nature of the topography, the slope and soil permeability in these regions. The data thus collected and the models so established have increased the understanding in these regions from a research perspective.<br>En ökad förståelse för hur grundvatten interagerar med ytvatten är av stor betydelse för att karakterisera underjordiska flödesprocesser. Omfattande undersökningar har tidigare genomförts för att bestämma de viktigaste faktorerna som styr de regionala konsekvenserna för cirkulationen av grundvattenflöde. Grundvattencirkulation uppstår på grund av variationer i grundvattentabellen (hydraulisk gradient) över den rumsliga skalan. Tidigare forskning belyste korrelationen mellan grundvattentabellen med både topografivariation och laddning från nederbörd. Denna studie syftar till att belysa effekterna av dessa gränsförhållanden. Fem avrinningsområden placerade över olika regioner i Sverige med olika topografiska, hydrologiska och meteorologiska egenskaper som beaktas för denna studie: Bodalsån, Forsmarksån, Tullstorpsån, Sävaån och Krycklan. Relevanta data samlades in och numeriska modeller sattes upp under steady-state-förhållanden för vart och ett av dessa avrinningsområden med användning av 3D Multiphysics COMSOL. Modeller konfigurerades för båda gränsförhållandena med 10 m nätupplösning. Grundvattenflödesprofiler längs avrinningsdjupet erhölls som resultat, där signifikanta skillnader observerades. Detta var främst förknippat med skillnaden i topografins natur och lutningen i dessa regioner. De data som samlats in och de så etablerade modellerna har ökat skapat en värdefull grund för vidare hydrologisk forskning i dessa regioner.
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Zugliani, Daniel. "Two-phase modelling of debris flow over composite topography: theoretical and numerical aspects." Doctoral thesis, Università degli studi di Trento, 2015. https://hdl.handle.net/11572/367641.
Full textAbstract:
In the mountain territory the majority of the population and of the productive activities are concentrated in the proximity of torrents or over alluvial fans. Here, when intense rainfall occurs, debris flow or hyper-concentrated flow events can produce serious problems to the population with possible casualties. On the other hand, the majority of these problems could be overcome with accurate hazard mapping, disaster prevention planning and mitigation structures (e.g. silt check dams, paved channels, weirs ...). Good and reliable mathematical and numerical models, able to accurately describe these phenomena are therefore necessary.
Debris flows and hyper-concentrated flows can be adequately represented by means of a mixture of a fluid (usually water) and a solid phase (granular sediment, e.g. sand, gravel ...), flowing over complex and composite topography. Complex topography is related to complicated bed elevation variety inasmuch as there are slopes, channels, human artifacts and so on. On the other hand, topography is composite because every type of flow can encounter two different bed behaviors: the mobile bed and the fixed bed. In the first case, mass can be exchanged between the bed and the flow, so the bottom elevation can change in time. In the second case (fixed bed case), this mass transfer is inhibited, due to the presence of a rigid bottom, such as bedrock or concrete, and the bottom cannot change in time. The first objective of the work presented in this thesis concerns the development of a new type of hyperbolic mathematical model for free-surface two-phase hyper-concentrated flows able to describe in a single way the fixed bed, the mobile bed and also the transition between them. The second objective, strictly connected with the first, is the development of a numerical scheme that implements this mathematical model in an accurate and efficient way. In the framework of finite-volume methods with Godunov approach, the fluxes are evaluated solving a Riemann Problem (RP). A RP is an initial value problem related to a set of PDEs equations wherein, in a certain point, there is a discontinuity separating different left and right initial constant states. However, if the topography is composite, a new type of Riemann problem, called Composite Riemann Problem (CRP), occurs. In a CRP, not only the initial constant states, but also the relevant PDEs systems change across the discontinuity. This additional complexity makes the general solution of the CRP quite challenging to obtain. The first part of the work is devoted to the derivation of the PDEs systems describing the fixed- and mobile-bed behaviors. Starting from the 3D discrete equations valid for each phase (continuous fluid and solid granular) and using suitable average processes the 3D continuous equations (continuous fluid and solid) are obtained. Introducing the shallow water approximation and performing the depth average process, the 2D fully two-phase models for free-surface flow over fixed- and mobile-bed are derived. The isokinetic approximation, which states the equality between the velocity of the solid phase and the liquid phase, is then used, ending up with the so-called two-phase isokinetic models. Finally, an exhaustive comparison between the fixed- and the mobile-bed fully two-phase models, the two-phase isokinetic models and others models proposed in the literature is presented.
The second part of the work concerns the definition and, mainly, the solution of the CRP from a mathematical point of view. Firstly, a general strategy for the CRP solution is developed. It allows to couple different hyperbolic systems that are physically compatible (e.g. fixed-bed with mobile-bed systems, free-surface flow with pressurized flow), also if they have a different number of equations. The resulting CRP solution is composed of a single PDEs system, called Composite PDEs system, whose properties, under some assumptions, degenerate to the properties of the original PDEs systems. The general strategy is developed using the simplest 1D isokinetic models for the fixed bed and the mobile bed (i.e. PDEs systems valid only for low concentration). Coherently with the generality of the CRP solution method, the low concentration constraint is then relaxed, ending up with a Composite PDEs system describing also high concentrated flows. From the numerical point of view, all the developed Composite systems are integrated using the finite-volume method with Godunov fluxes. These fluxes are evaluated using three different approximated Riemann solvers: the Generalized Roe solver, the LHLL solver and the Universal Osher solver. All the solvers are analyzed and an exhaustive comparison between them is performed, highlighting pros and cons. The schemes are second order accurate in space and time, and this has been achieved by means of the MUSCL approach. Finally numerical schemes have been parallelized using OpenMP standard. All the models are then tested comparing analytical and numerical solutions. The results are satisfactory, with an accurate agreement between the two solutions in the majority of the physically-based test cases. There is only some small issue when the simulations are performed in a few resonant cases. However, these problems arise in not realistic situations, so it is impossible to encounter them in real situations. Also a realistic application is presented (i.e. the evolution of a trench over partially paved channel), proving the capabilities of both the mathematical approach and the numerical scheme.
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Zugliani, Daniel. "Two-phase modelling of debris flow over composite topography: theoretical and numerical aspects." Doctoral thesis, University of Trento, 2015. http://eprints-phd.biblio.unitn.it/1497/1/PhD_Thesis_Zugliani_Daniel.pdf.
Full textAbstract:
In the mountain territory the majority of the population and of the productive activities are concentrated in the proximity of torrents or over alluvial fans. Here, when intense rainfall occurs, debris flow or hyper-concentrated flow events can produce serious problems to the population with possible casualties. On the other hand, the majority of these problems could be overcome with accurate hazard mapping, disaster prevention planning and mitigation structures (e.g. silt check dams, paved channels, weirs ...). Good and reliable mathematical and numerical models, able to accurately describe these phenomena are therefore necessary.
Debris flows and hyper-concentrated flows can be adequately represented by means of a mixture of a fluid (usually water) and a solid phase (granular sediment, e.g. sand, gravel ...), flowing over complex and composite topography. Complex topography is related to complicated bed elevation variety inasmuch as there are slopes, channels, human artifacts and so on. On the other hand, topography is composite because every type of flow can encounter two different bed behaviors: the mobile bed and the fixed bed. In the first case, mass can be exchanged between the bed and the flow, so the bottom elevation can change in time. In the second case (fixed bed case), this mass transfer is inhibited, due to the presence of a rigid bottom, such as bedrock or concrete, and the bottom cannot change in time. The first objective of the work presented in this thesis concerns the development of a new type of hyperbolic mathematical model for free-surface two-phase hyper-concentrated flows able to describe in a single way the fixed bed, the mobile bed and also the transition between them. The second objective, strictly connected with the first, is the development of a numerical scheme that implements this mathematical model in an accurate and efficient way. In the framework of finite-volume methods with Godunov approach, the fluxes are evaluated solving a Riemann Problem (RP). A RP is an initial value problem related to a set of PDEs equations wherein, in a certain point, there is a discontinuity separating different left and right initial constant states. However, if the topography is composite, a new type of Riemann problem, called Composite Riemann Problem (CRP), occurs. In a CRP, not only the initial constant states, but also the relevant PDEs systems change across the discontinuity. This additional complexity makes the general solution of the CRP quite challenging to obtain. The first part of the work is devoted to the derivation of the PDEs systems describing the fixed- and mobile-bed behaviors. Starting from the 3D discrete equations valid for each phase (continuous fluid and solid granular) and using suitable average processes the 3D continuous equations (continuous fluid and solid) are obtained. Introducing the shallow water approximation and performing the depth average process, the 2D fully two-phase models for free-surface flow over fixed- and mobile-bed are derived. The isokinetic approximation, which states the equality between the velocity of the solid phase and the liquid phase, is then used, ending up with the so-called two-phase isokinetic models. Finally, an exhaustive comparison between the fixed- and the mobile-bed fully two-phase models, the two-phase isokinetic models and others models proposed in the literature is presented.
The second part of the work concerns the definition and, mainly, the solution of the CRP from a mathematical point of view. Firstly, a general strategy for the CRP solution is developed. It allows to couple different hyperbolic systems that are physically compatible (e.g. fixed-bed with mobile-bed systems, free-surface flow with pressurized flow), also if they have a different number of equations. The resulting CRP solution is composed of a single PDEs system, called Composite PDEs system, whose properties, under some assumptions, degenerate to the properties of the original PDEs systems. The general strategy is developed using the simplest 1D isokinetic models for the fixed bed and the mobile bed (i.e. PDEs systems valid only for low concentration). Coherently with the generality of the CRP solution method, the low concentration constraint is then relaxed, ending up with a Composite PDEs system describing also high concentrated flows. From the numerical point of view, all the developed Composite systems are integrated using the finite-volume method with Godunov fluxes. These fluxes are evaluated using three different approximated Riemann solvers: the Generalized Roe solver, the LHLL solver and the Universal Osher solver. All the solvers are analyzed and an exhaustive comparison between them is performed, highlighting pros and cons. The schemes are second order accurate in space and time, and this has been achieved by means of the MUSCL approach. Finally numerical schemes have been parallelized using OpenMP standard. All the models are then tested comparing analytical and numerical solutions. The results are satisfactory, with an accurate agreement between the two solutions in the majority of the physically-based test cases. There is only some small issue when the simulations are performed in a few resonant cases. However, these problems arise in not realistic situations, so it is impossible to encounter them in real situations. Also a realistic application is presented (i.e. the evolution of a trench over partially paved channel), proving the capabilities of both the mathematical approach and the numerical scheme.