Dissertations / Theses on the topic 'Geophysical and environmental fluid flows'

Small scale laboratory experiments were conducted to study the dynamic mor- phology and rheological behaviour of fluid-particle mixtures, such as snout-body architecture, levee formation, deposition and particle segregation effects. Debris flows consist of an agitated mixture of rock and sediment saturated with water. They are mobilized under the influence of gravity from hill slopes and channels and can reach long run-out distance and have extremely destructive power. Better understanding of the mechanisms that govern these flows is required to assess and mitigate the hazard of debris flows and similar geophysical flows. Debris flow models are required to accurately deal with evolving behaviours in space and time, to be able to predict flow height, velocity profiles and run-out distances and shapes. The evolution of laboratory debris flows, both dry glass beads and mixtures with water or glycerol, released from behind a lock gate to flow down an inclined flume, was observed through the channel side wall and captured with high speed video and PIV analysis to provide velocity profiles through out the flow depth. Pore pressure and the normal and shear stress at the base of the flow were also measured. Distinct regions were characterized by the non-fluctuating region and the in- termittent granular cloud surrounding the flows. The extent of these regions was shown to be related to flow properties. The separation of these two regions allowed the systematic definition of bulk flow characteristics such as characteristic height and flow front position. Laboratory flows showed variations in morphology and rheological characteristics under the influence of particle size, roughness element diameter, interstitial fluid viscosity and solid volume fraction. Mono-dispersed and poly-dispersed components mixed with liquids without fine sediments, reveal a head and body structure and an appearance similar to the classic anatomy of real debris flows. Unsaturated fronts were observed in mono-dispersed flows, suggesting that particle segregation is not the only mechanism. A numerical simulation of laboratory debris flows using the computer model RAMMS (RApid Mass Movements Simulation) was tested with dry laboratory flows, showing close similarity to calculated mean velocities.

An alternative formulation of the governing equations of a dynamical system, called the multi-scale localized perturbation method, is introduced and derived for the purpose of solving complex geophysical flow problems. Simulation variables are decomposed into background and perturbation components, then assumptions are made about the evolution of these components within the context of an environmental flow in order to close the system. Once closed, the original governing equations become a set of one-way coupled governing equations called the "delta form" of the governing equations for short, with one equation describing the evolution of the background component and the other describing the evolution of the perturbation component. One-way interaction which arises due to non-linearity in the original differential equations appears in this second equation, allowing the background fields to influence the evolution of a perturbation. Several solution methods for this system of equations are then proposed. Advantages of the delta form include the ability to specify a complex, temporally- and spatially-varying background field separate from a perturbation introduced into the system, including those created by natural or man-made sources, which enhances visualization of the perturbation as it evolves in time and space. The delta form is also shown to be a tool which can be used to simplify simulation setup. Implementation of the delta form of the incompressible URANS equations with turbulence model and scalar transport within OpenFOAM is then documented, followed by verification cases. A stratified wake collapse case in a domain containing a background shear layer is then presented, showing how complex internal gravity wave-shear layer interactions are retained and easily observed in spite of the variable decomposition. The multi-scale localized perturbation method shows promise for geophysical flow problems, particularly multi-scale simulation involving the interaction of large-scale natural flows with small-scale flows generated by man-made structures.
Master of Science
Natural flows, such as those in our oceans and atmosphere, are seen everywhere and affect human life and structures to an amazing degree. Study of these complex flows requires special care be taken to ensure that mathematical equations correctly approximate them and that computers are programmed to correctly solve these equations. This is no different for researchers and engineers interested in studying how man-made flows, such as one generated by the wake of a plane, wind turbine, cruise ship, or sewage outflow pipe, interact with natural flows found around the world. These interactions may yield complex phenomena that may not otherwise be observed in the natural flows alone. The natural and artificial flows may also mix together, rendering it difficult to study just one of them. The multi-scale localized perturbation method is devised to aid in the simulation and study of the interactions between these natural and man-made flows. Well-known equations of fluid dynamics are modified so that the natural and man-made flows are separated and tracked independently, which gives researchers a clear view of the current state of a region of air or water all while retaining most, if not all, of the complex physics which may be of interest. Once the multi-scale localized perturbation method is derived, its mathematical equations are then translated into code for OpenFOAM, an open-source software toolkit designed to simulate fluid flows. This code is then tested by running simulations to provide a sanity check and verify that the new form of the equations of fluid dynamics have been programmed correctly, then another, more complicated simulation is run to showcase the benefits of the multi-scale localized perturbation method. This simulation shows some of the complex fluid phenomena that may be seen in nature, yet through the multi-scale localized perturbation method, it is easy to view where the man-made flows end and where the natural flows begin. The complex interactions between the natural flow and the artificial flow are retained in spite of separating the flow into two parts, and setting up the simulation is simplified by this separation. Potential uses of the multi-scale localized perturbation method include multi-scale simulations, where researchers simulate natural flow over a large area of land or ocean, then use this simulation data for a second, small-scale simulation which covers an area within the large-scale simulation. An example of this would be simulating wind currents across a continent to find a potential location for a wind turbine farm, then zooming in on that location and finding the optimal spacing for wind turbines at this location while using the large-scale simulation data to provide realistic wind conditions at many different heights above the ground. Overall, the multi-scale localized perturbation method has the potential to be a powerful tool for researchers whose interest is flows in the ocean and atmosphere, and how these natural flows interact with flows created by artificial means.

The accurate and efficient numerical simulation of geophysical flows is of great interest in numerical weather prediction and climate modeling as well as in numerous critical areas and industries, such as agriculture, construction, tourism, transportation, weather-related disaster management, and sustainable energy technologies. Oceanic and atmospheric flows display an enormous range of temporal and spatial scales, from seconds to decades and from centimeters to thousands of kilometers, respectively. Scale interactions, both spatial and temporal, are the dominant feature of all aspects of general circulation models in geophysical fluid dynamics. In this thesis, to decrease the cost for these geophysical flow computations, several types of multiscale methods were systematically developed and tested for a variety of physical settings including barotropic and stratified wind-driven large scale ocean circulation models, decaying and forced two-dimensional turbulence simulations, as well as several benchmark incompressible flow problems in two and three dimensions. The new models proposed here are based on two classes of modern multiscale methods: (i) interpolation based approaches in the context of the multigrid/multiresolution methodologies, and (ii) deconvolution based spatial filtering approaches in the context of large eddy simulation techniques. In the first case, we developed a coarse-grid projection method that uses simple interpolation schemes to go between the two components of the problem, in which the solution algorithms have different levels of complexity. In the second case, the use of approximate deconvolution closure modeling strategies was implemented for large eddy simulations of large-scale turbulent geophysical flows. The numerical assessment of these approaches showed that both the coarse-grid projection and approximate deconvolution methods could represent viable tools for computing more realistic turbulent geophysical flows that provide significant increases in accuracy and computational efficiency over conventional methods.
Ph. D.

In this thesis, parameterizations of non-linear interactions in quasigeostrophic (QG) flows for severely truncated models (STM) and Large Eddy Simulations (LES) are studied. Firstly, using Direct Numerical Simulations (DNS), atmospheric barotropic flows over topography are examined, and it is established that such flows exhibit multiple equilibrium states for a wide range of parameters. A STM is then constructed, consisting of the large scale zonal flow and a topographic mode. It is shown that, qualitatively, this system behaves similarly to the DNS as far as the interaction between the zonal flow and topography is concerned, and, in particular, exhibits multiple equilibrium states. By fitting the analytical form of the topographic stationary wave amplitude, obtained from the STM, to the results obtained from DNS, renormalized dissipation and rotation parameters are obtained. The usage of renormalized parameters in the STM results in better quantitative agreement with the DNS.¶ In the second type of problem, subgrid-scale parameterizations in LES are investigated with both atmospheric and oceanic parameters. This is in the context of two-level QG flows on the sphere, mostly, but not exclusively, employing a spherical harmonic triangular truncation at wavenumber 63 (T63) or higher. The methodology that is used is spectral, and is motivated by the stochastic representation of statistical closure theory, with the ‘damping’ and forcing covariance, representing backscatter, determined from the statistics of DNS. The damping and forcing covariance are formulated as 2 × 2 matrices for each wavenumber. As well as the transient subgrid tendency, the mean subgrid tendency is needed in the LES when the energy injection region is unresolved; this is also calculated from the statistics of the DNS. For comparison, a deterministic parameterization scheme consisting of 2×2 ‘damping’ parameters, which are calculated from the statistics of DNS, has been constructed. The main difference between atmospheric and oceanic flows, in this thesis, is that the atmospheric LES completely resolves the deformation scale, the energy and enstrophy injection region, and the truncation scale is spectrally distant from it, being well in the enstrophy cascade inertial range. In oceanic flows, however, the truncation scale is in the vicinity of the injection scale, at least for the parameters chosen, and is therefore not in an inertial range. A lower resolution oceanic LES at T15 is also examined, in which case the injection region is not resolved at all.¶ For atmospheric flows, it is found that, at T63, the matrix parameters are practically diagonal so that stratified atmospheric flows at these resolutions may be treated as uncoupled layers as far as subgrid-scale parameterizations are concerned. It is also found that the damping parameters are relatively independent of the (vertical) level, but the backscatter parameters are proportional to the subgrid flux in a given level. The stochastic and deterministic parameterization schemes give comparably good results relative to the DNS. For oceanic flows, it is found that the full matrix structure of the parameters must be used. Furthermore, it is found that there is a strong injection of barotropic energy from the subgrid scales, due to the unresolved, or partially resolved, baroclinic instability injection scales. It is found that the deterministic parameterization is too numerically unstable to be of use in the LES, and instead the stochastic parameterization must be used to obtain good agreement with the DNS. The subgrid tendency of the ensemble mean flow is also needed in some problems, and is found to reduce the available potential energy of the flow.

The Seattle District wants to better manage the Ballard Locks and structures along the Lake Washington Ship Canal (LWSC) in a way that will maintain the environmental sustainability and biodiversity in the area. Due to strict salt water intrusion regulations in the LWSC, the Seattle District is working on upgrading their management practices such that they will resolve two inter-related problems. First, to improve the fish passage conditions for migrating salmon; and second, to learn how to better manage the salt wedge that forms and intrudes upstream. Based on the hydrodynamic and water quality results that are produced by this research, the Engineer Research and Development Center (ERDC) Portland Office will use their Eulerian-Lagrangian-Agent-Model (ELAM) to analyze fish patterns, looking for the most beneficial management schemes that assist salmon in migrating upstream. This research implemented CFD engineering techniques to help better understand the effectiveness of the hydraulic structures in the area, as well as come up with management practices that both mitigate the salt water intrusion from Puget Sound, and improve the migrating passages for salmon.

The design of channels or hydraulic structures requires the correct prediction of flow properties such as depth of flow. In uniform open channel flows, a one dimensional (1-D) approach which assumes hydrostatic pressure distribution, negligible air entrainment and uniform velocity in the direction of flow is often used. Spatially varied flow (SVF) is a special type of open channel flow in which the discharge increases or decreases along the channel due to lateral inflow or outflow, respectively. As a result, this intricate flow is associated with momentous turbulence and velocity fluctuations in all three directions of flow. Researchers have proven that using the 1-D approach for predicting SVF properties yields erroneous results. This thesis details research conducted (i) to improve the accuracy of the current one-dimensional equation, (ii) to quantify the amount of oxygen transferred by lateral inflow and (iii) to predict turbulence characteristics using three-dimensional turbulence model. First, it is proposed that SVF due to lateral inflow, which is the focus of this study, can be likened to multiple jets in crossflow and open channels with emergent vegetation. In these two cases, the multiple jet and the vegetation stems resemble a solid cylindrical object blocking the crossflow thus effects of the drag force are vital. Similar to open channel with emergent vegetation studies, a new equation accounting for the drag force was developed and tested for different arrangements of SVF. Results indicated significant improvements in predicting water surface profiles. Second, similar to weir flow the amount of oxygen transferred by lateral inflow was measured under different flow conditions and various modes of lateral inflow entry to the channel. The amount of dissolved oxygen (DO) in a body is vital for improving water quality. Results indicated that increasing jet velocity, discharge height and number of jets at optimum water depth in the receiving channel enhances oxygen transfer. Finally, three-dimensional computational fluid dynamics (CFD) analysis of an open channel receiving inflow from multiple jets in tandem issuing from a circular nozzle was conducted using the relatively low cost Reynolds-averaged Navier-Stokes (RANS) models namely the realizable k-ε, shear stress transport (SST) k-ω and the Reynolds stress model (RSM) based on their prominence in jet in crossflow studies. RANS models failed to predict turbulence characteristics within the lateral inflow region although average velocities in the longitudinal direction were acceptable. On the leeward side of the jet, RANS models failed to capture the downward velocity vectors resulting in major deviations in vertical velocity. It can be concluded that standard turbulence models are incapable of predicting the complex characteristics of SVF. However, turbulence models remain superior to the 1-D approach.

Étudier les ondes internes est crucial pour comprendre le mélange dans l'océan. Dans cette thèse, un attracteur d'ondes 2D est tout d'abord simulé de manière directe, appuyé par une bonne comparaison avec une expérience préexistante. Nous dérivons un modèle simple de la largeur de l'attracteur et mettons en évidence des effets non-linéaires. Nous réalisons dans une deuxième partie une étude expérimentale de la réflexion d'ondes planes sur une paroi inclinée. Les résonances prédites entre différents harmoniques n'apparaissent pas mais en revanche, un fort écoulement moyen horizontal apparaît, courbant les caractéristiques des ondes par effet Doppler. 70 à 80% du flux d'énergie incident sont dissipés ou convertis en écoulement moyen, ce dernier semblant alimenté par la dissipation des ondes. La génération d'ondes solitaires consécutive à la réflexion d'ondes sur une pycnocline est ensuite étudiée numériquement dans la troisième partie. Dans un premier temps, une étude académique, 2D est réalisée à l'aide de simulations directes. Nous montrons que des ondes solitaires de différents modes et piégées dans la pycnocline peuvent être générées. Deux critères pour comprendre la sélection d'un mode donné, l'un portant sur les différentes vitesses de phase, l'autre sur des arguments géométriques, sont définis. Ces critères sont dans un second temps comparés aux conditions du Golfe de Gascogne en été. Nous montrons qu'un rayon d'ondes internes seul ne peut générer des ondes solitaires correspondant aux observations, ce qui est corrigé en tenant compte de l'écoulement présent dans la pycnocline et indépendant du rayon d'ondes internes
Internal wave studies are crucial to the understanding of deep-ocean mixing. In this thesis, we first describe a 2D direct numerical simulation of a wave attractor and validate it against pre-existing experimental data. We then propose a model for the thickness of the attractor along the direction of propagation of energy. We eventually study nonlinear effects induced by the attractor. In a second part, we describe an experimental study of the reflection of plane waves on a sloping wall. Unexpectedly, resonances between different wave harmonics are not observed. However, a horizontal mean flow is generated and the wave characteristics are curved, due to the Doppler effect. 70 to 80% of the incident energy flux is dissipated and transferred to the mean flow, the latter being seemingly generated by wave dissipation. In a third part, we perform a numerical study of the generation of internal solitary waves by an impinging wave beam. We first present direct numerical simulations of this process and show that different solitary wave modes can be excited. Criteria for the selection of a particular mode are put forward, the first one being in terms of phase speeds and the second one based on geometrical arguments. Results are compared with the configuration of the Bay of Biscay in summer. We show that a beam impinging on a thermocline initially at rest cannot generate solitary waves which features agree with oceanic observations. This can be corrected by considering the background flow around the thermocline as found in the Bay of Biscay and independent of the internal wave beam

In addition, the vanishing viscousity limit of the solutions for viscous lake equations with the Navier type boundary conditions is obtained for both the smooth and non-smooth initial data.
The aim of the thesis is to understand the dynamics and interactions between the Ekman layer and thermal layer which are very important issues in the studies of geophysical flows. We obtain some new results on the primitive equations of the atmosphere and the incompressible Navier-Stokes equations with rotating terms. We study the asymptotic limits of the solutions to the initial boundary value problem for the three dimensional primitive equations. We have constructed the asymptotic ansatz which is uniformly valid up to the boundary to derive the quasi-geostrophic equations and the corresponding boundary layer systems. These equations are also important and widely studied in the geophysical flows. The uniform convergence to the solutions for quasi-geostrophic equations is obtained rigorously.
Niu Dongjuan.
"June 2006."
Adviser: Zhouping Xin.
Source: Dissertation Abstracts International, Volume: 68-03, Section: B, page: 1675.
Thesis (Ph.D.)--Chinese University of Hong Kong, 2006.
Includes bibliographical references (p. 96-106).
Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Abstracts in English and Chinese.
School code: 1307.

Thesis (Ph. D.)--University of Illinois at Urbana-Champaign, 2006.
Source: Dissertation Abstracts International, Volume: 67-11, Section: B, page: 6465. Adviser: Nigel Goldenfeld. Includes bibliographical references (leaves 243-257). Available on microfilm from Pro Quest Information and Learning.

The effect of rotation on the stability of multiple jets in planetary atmospheres is system- atically investigated. Typically in Jovian planetary atmospheres, multiple zonal jets have been observed and their morphology has been systematically studied. The formation of jets has always been viewed as a nonlinear problem where most work has followed from the ideas of potential vorticity (PV) homogenization or turbulent mixing on a β-plane. In our present work, we have aimed to look at the linear stability of multiple jets in a geophysical fluid, and hope to add further insight into the observed jet profiles in β-plane turbulence. In addition, we also study the evolution and life-cycle of these jets as they interact with each other in a non linear fashion. We begin with the linear stability of the \Bickley jet" using the linearized shallow water quasigeostrophic (QG) equations. We have included a finite deformation radius in our calculations to partially mimic the effects of compressibility. A family of synthetically generated velocity profiles with east-west jets are then studied. In particular, a variety of flow configurations with two jets have been considered with a parameter sweep across jet separation, relative jet strength and thickness. As a broad observation, it is noted that an asymmetric east-west jet profile with a stronger and sharper eastward jet is the most stable of all the profiles considered, and a finite deformation radius further stabilizes such profiles. More realistic jet profiles have also been considered and the role of a finite deformation radius in stabilizing such jets is elucidated. We also examined the nonlinear evolution of multiple jets in a periodic domain and in a channel geometry, as we undertake freely decaying long time simulations of the governing QG equation. As per the \Selective Decay" principle we observe that arbitrary initial conditions approach the flow configuration of the prescribed \suitable end states". In addition, we have shown how a finite deformation length scale modifies these \suitable end states". As a broad observation, we have noted that a linearly unstable jet flow configuration, in the presence of β, breaks down into turbulence and reforms into a more asymmetric jet profile with a stronger and sharper eastward jet. The inclusion of a finite deformation length scale in our calculations, is observed to suppress such jet formation. Similar numerical experiments have been performed in a channel and the results have been compared. Chiefly, for the end states, the nature of the observed jet asymmetry is reversed, i.e., the westward jets are observed to be stronger in a channel.

Stably stratified flows are common in the environment such as in the atmospheric· boundary layer, the oceans, lakes and estuaries. Understanding mixing and dispersion in these flows is of fundamental importance in applications such as the prediction of pollution dispersion and for weather and climate prediction/models. Mixing efficiency in stratified flows is a measure of the proportion of the turbulent kinetic energy that goes into increasing the potential energy of the fluid by irreversible mixing. This can be important for parameterizing the effects of mixing in stratified flows. In this research, fully resolved direct numerical simulations (DNS) of the Navier-Stokes equations are used to study transient turbulent mixing events. The breaking of internal waves in the atmosphere could be a source of such episodic events in the environment. The simulations have been used to investigate the mixing efficiency (integrated over the duration of the event) as a function of the initial turbulence Richardson number Ri = N2L2/U2, where N is the buoyancy frequency, L is the turbulence length scale, and u is the turbulence velocity scale. Molecular effects on the mixing efficiency have been investigated by varying the Prandtl number Pr = V/K, where v is the viscosity and K is the scalar diffusivity. Comparison of the DNS results with grid turbulence experiments has been carried out. There is broad qualitative agreement between the experimental and DNS results.· However the experiments suggest a maximum mixing efficiency of 6% while our DNS gives values about five times higher. Reasons for this discrepancy are investigated. The mixing efficiency has also been determined using linear theory. It is found that the results obtained for the very stable cases converge on those obtained from DNS suggesting that strongly stratified flows exhibit linear behaviour. Lagrangian analysis of mixing is fundamental in understanding turbulent diffusion and mixing. Dispersion models such as that of Pearson, Puttock & Hunt (1983) are based on a Lagrangian approach. A particle-tracking algorithm (using a cubic spline interpolation scheme following Yeung &Pope, 1988) was developed and incorporated into the DNS code to enable an investigation into the fundamental aspects of mixing and diffusion from a Lagrangian perspective following fluid elements. From the simulations, the ensemble averaged rate of mixing as a function of time indicates clearly that nearly all the mixing in these flows occurs within times of order 3 Vu. The mean square vertical displacement statistics show how the stable stratification severely inhibits the vertical displacement of fluid elements but has no effect on displacements in the transverse direction. This is consistent with the Pearson, Puttock & Hunt model. The important link that asymptotic value of the mean square vertical displacement is a measure of the total irreversible mixing that has occurred in the flow is made. However the results show that the change in density of the fluid elements is only weakly correlated to the density fluctuations during the time when most of the mixing occurs, which contradicts a key modeling assumption of the PPH theory. Improvements to the parameterization of this mixing are investigated. Flow structures in stably stratified turbulence were examined using flow visualization software. The turbulence structure for strong stratification resembles randomly scattered pancakes that are flattened in the horizontal plane. It appears that overturning motions are the main mechanism by which mixing occurs in these flows.
Thesis (M.Sc.Eng.)-University of Natal, Durban, 2002.

This dissertation includes two fluid dynamics studies that involve fluid flows on vastly different scales, and therefore vastly different physics. The first study is of bacterial swimming using a flagellum for propulsive motion. Because bacteria are only about 10 [micrometers] in length, they swim in a very low Reynolds number (10⁻⁴) world, which is described by the linear set of governing equations known as the Stokes equations, that are a simplified version of the Navier-Stokes equations. The second study is of harmonic generation from nonlinear effects in internal, ocean-like wave beams that reflect from boundaries in a density stratified fluid. Internal wave reflection is an important oceanic process and may help sustain ocean circulation and affect global weather patterns. Such ocean processes have typical Reynold's numbers of 10¹⁰ or more and are only described by the full, nonlinear Navier-Stokes equations. In the low Reynolds number study, I examine theories by Gray et al.(1956) and Lighthill (1975) that describe swimming microorganisms using a helical flagellum for propulsive motion. I determine the resistance matrix, which can fully describe the dynamics of a flagellum, for flagella with different geometries, defined by: filament radius a, helical radius R, helical pitch [lambda], and axial length L. I use laboratory experiments and numerical simulations conducted in collaboration with Dr. Hepeng Zhang. The experiments, conducted with assistance from a fellow graduate student Chih-Hung Chen, use macroscopic scale models of bacterial flagella in a bath of highly viscous silicone oil. Numerical simulations use the Regularized Stokeslet method, which approximates the Stokeslet representation of an immersed body in a low Reynolds number flow. My study covers a biologically relevant parameter regime: 1/10R < a < 1/25R, R < [lambda] < 20R, and 2R< L <40R. I determine the three elements of the resistance matrix by measuring propulsive force and torque generated by a rotating, non-translating flagellum, and the drag force on a translating, non-rotating flagellum. I investigate the dependences of the resistance matrix elements on both the flagellum's axial length and its wavelength. The experimental and numerical results are in excellent agreement, but they compare poorly with the predictions of resistive force theory. The theory's neglect of hydrodynamic interactions is the source of the discrepancies in both the length dependence and wavelength dependence studies. I show that the experimental and simulation data scale as L/ln(L/r), a scaling analytically derived from slender body theory by my other collaborator Dr. Bin Liu. This logarithmic scaling is new and missing from the widely used resistive force theory. Dr. Zhang's work also includes a new parameterized version of resistive force theory. The second part of the dissertation is a study of harmonic generation by internal waves reflected from boundaries. I conduct laboratory experiments and two-dimensional numerical simulations of the Navier-Stokes equations to determine the value of the topographic slope that gives the most intense generation of second harmonic waves in the reflection process. The results from my experiments and simulations agree well but differ markedly from theoretical predictions by Thorpe (1987) and by Tabaei et al. (2005), except for nearly inviscid, weakly nonlinear flow. However, even for weakly nonlinear flow (where the dimensionless Dauxois-Young amplitude parameter value is only 0.01), I find that the ratio of the reflected wavenumber to the incoming wavenumber is very different from the prediction of weakly nonlinear theory. Further, I observe that for incident beams with a wide range of angles, frequencies, and intensities, the second harmonic beam produced in reflection has a maximum intensity when its width is the same as the width of the incident beam. This observation yields a prediction for the angle corresponding to the maximum in second harmonic intensity that is in excellent accord with my results from experiments and numerical simulations.
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Flow instabilities occur at all scales in planetary systems. In this thesis we examine three cases of such instabilities, on three very different length scales. In the first part, we test the idea that Archean granite-greenstone belts (GGBs) form by crustal diapirism, or Rayleigh-Taylor instabilities. GGBs are characterized by large granitic domes (50-100 km in diameter) embedded in narrow keel-shaped greenstones. They are ubiquitous in Archean (> 2.5 Ga) terrains, but rare thereafter. We performed finite element calculations for a visco-elastic, temperature-dependent, non-Newtonian crust under conditions appropriate for the Archean, which show that dense low-viscosity volcanics overlying a felsic basement will overturn diapirically in as little as 10 Ma, displacing as much as 60 % of the volcanics to the lower crust. This surprisingly fast overturn rate suggests that diapiric overturn dominated crustal tectonics in the hot conditions of the Early Earth, becoming less important as the Earth cooled. Moreover, the deposition of large volumes of wet basaltic volcanics to the lower crust may provide the source for the formation of the distinctly Archean granitic rocks which dominate Earth's oldest continents. The second part examines the origin of Venusian coronae, circular volcanic features unique to Venus. Coronae are thought to result from small instabilities (diapirs) from the core-mantle boundary, which are typical of stagnant-lid convection. However, most young coronae are located in a region surrounded by long-lived hotspots, typical of a more active style of mantle convection. Using analogue experiments in corn syrup heated from below, we show that the co-existence of diapirs and long-lived mantle plumes are a direct consequence of the catastrophic overturn of the cold Venusian lithosphere thought to have occurred ~ 700 Ma ago. In the last part we analyze the thermal effect of fluid flow through a full-scale experiment testing clay and concrete tunnel seals in a Deep Geological Repository for nuclear was finite element software, we were able to show that the formation of fissures in the heated chamber between the two seals effectively limited heat flow, and could explain the discrepancy between the predicted and measured temperatures.

In this thesis, parameterizations of non-linear interactions in quasigeostrophic (QG) flows for severely truncated models (STM) and Large Eddy Simulations (LES) are studied. Firstly, using Direct Numerical Simulations (DNS), atmospheric barotropic flows over topography are examined, and it is established that such flows exhibit multiple equilibrium states for a wide range of parameters. A STM is then constructed, consisting of the large scale zonal flow and a topographic mode. It is shown that, qualitatively, this system behaves similarly to the DNS as far as the interaction between the zonal flow and topography is concerned, and, in particular, exhibits multiple equilibrium states. By fitting the analytical form of the topographic stationary wave amplitude, obtained from the STM, to the results obtained from DNS, renormalized dissipation and rotation parameters are obtained. The usage of renormalized parameters in the STM results in better quantitative agreement with the DNS.¶ In the second type of problem, subgrid-scale parameterizations in LES are investigated with both atmospheric and oceanic parameters. ...

It is often desirable to study simulated turbulent flows at steady state even if the flow has no inherent source of turbulence kinetic energy. Doing so requires a numerical forcing scheme and various methods have been studied extensively for turbulence that is isotropic and homogeneous in three dimensions. A review of these existing schemes is used to form a framework for more general forcing methods. In this framework, the problem of developing a forcing scheme in Fourier space is abstracted into the two problems of (1) prescribing the spectrum of the input power and (2) specifying a force that has the desired characteristics and that adds energy to the flow with the correct spectrum. The framework is used to construct three forcing schemes for horizontally homogeneous and isotropic, vertically stratified turbulence. These schemes are implemented in large-eddy simulations and their characteristics analyzed. Which method is “best” depends on the purpose of the simulations, but the framework for specifying forcing schemes enables a systematic approach for identifying a method appropriate for a particular application.