Dissertations / Theses on the topic 'Stratified boundary layer'

Thesis (Ph. D.)--University of California, San Diego, 2008.
Title from first page of PDF file (viewed March 24, 2008). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references (p. 205-212).

La capa límit atmosfèrica és l'àrea directament influenciada per la presència de la superfície de la terra i la seva alçada és d'uns centenars de metres a uns pocs quilòmetres. Durant el vespre, el refredament radiatiu estratifica establement l'aire prop del sòl i es forma el que es coneix com a Capa Límit Estable (CLE). D'avui en dia, la CLE és un règim que encara no està prou ben caracteritzat. La turbulència, que no és homogènia ni isòtropa, i la gran importància dels efectes locals com l'orografia, entre d'altres factors, dificulten l'estudi d'aquest règim. Per aquest motiu, la CLE és objecte d'especial atenció, sobretot a l'hora de millorar la seva representació en models tant de temps com de clima.

Aquest treball es centra en l'estudi de la CLE mitjançant 3 eines diferents: 1) simulacions explícites de grans remolins (més conegudes com a simulacions LES), per determinar el comportament dels moviments turbulents, on les resolucions són de l'ordre de metres; 2) simulacions mesoscalars, per caracteritzar els efectes locals, on les resolucions són de l'ordre de kilòmetres; 3) anàlisi de les observacions sota aquestes condicions per tal de caracteritzar i entendre millor els fenòmens observats.

En primer lloc s'estudia el rang d'estabilitats a on el model LES, que considera la teoria de Kolmogorov per la dissipació de l'energia, funciona correctament. Els resultats del model són realistes tal com mostra la seva comparació amb les mesures de dues campanyes experimentals (SABLES-98 i CASES-99). Per explorar més a fons els resultats LES i per comparar-los amb les mesures s'han utilitzat les Funcions de Distribució de Probabilitat (PDF). Aquests resultats LES són també comparables als obtinguts amb altres models LES, tal com mostra la intercomparació de models LES, més coneguda com a GABLS.

Un cop desenvolupades totes les eines necessàries es fa un LES d'un cas més realista, basat en les observacions d'un màxim de vent de capes baixes (més conegut com a Low-Level Jet, LLJ). L'anàlisi combinat dels resultats LES i les mesures permet entendre millor els processos de barreja que tenen lloc a través de la inversió. Finalment, la contribució dels efectes locals s'estudia mitjançant les simulacions mesoscalars, en aquest cas centrades a l'illa de Mallorca. Durant el vespre es veu com les circulacions locals es desenvolupen a les conques (de longitud al voltant de 25km), formant-se, per exemple, vents catabàtics o LLJ com l'estudiat anteriorment. En aquest cas les simulacions es verifiquen amb imatges de satèl·lit NOAA i observacions de les estacions automàtiques de mesures, donant resultats semblants.
The atmospheric boundary layer is the area directly influenced by the presence of the Earth's surface and its height is from hundreds of meters to few kilometres. During the night, the radiative cooling stratifies the layer close to the surface and it forms the Stably-stratified Atmospheric Boundary Layer (SBL). Nowadays, the SBL is a regime not well enough characterized, yet. Turbulence, which is not homogeneous either isotropic, and the great importance of the local effects, like the orography, among other factors, make the SBL be a difficult regime to study. Even so, the SBL is an object of special attention, especially when improving its representation in numerical prediction models or climate models.

This work focuses on the study of the SBL through 3 different tools: 1) Large-Eddy Simulations (LES), to determine the turbulent motions, where the resolutions are about 1m; 2) Mesoscale simulations, to characterize the local effects, where resolutions are about 1km; 3) Analysis of the observations under these conditions in order to better characterize and understand the observed phenomena.

In first place, it is studied the range of stabilities where the LES model, that considers the Kolmogorov theory for the dissipation of the energy, works correctly. The results are realistic as the comparison with measures from two experimental campaigns (SABLES-98 and CASES-99) shows. To explore the results more thoroughly, and to compare the LES results to the measurements, the Probability Density Functions (PDF) have been used. The LES results are also comparable to the ones obtained with other LES models, as the intercomparison of different LES models show, better known as GABLS.

Then, a more realistic case is performed using the LES model, based on observations of a Low-Level Jet (LLJ). The combined inspection of the LES results and the observations allow to better understand the mixing processes that take place through the inversion layer. Finally, the contribution of the local effects is studied through a mesoscale simulation. Here the attention is focused on the Mallorca Island. During the night, the model is able to reproduce the local circulations is a basin of a characteristic size of 25km. The main features obtained previously from the LES of the LLJ are also reproduced by the mesoscale model. These runs are verified with NOAA satellite images and observations from the automatic surface weather stations, giving that the model is able to reproduce realistic results.

The aim of this thesis is the study of the exchange processes at atmosphere/biosphere interface, with a particular focus on momentum and heat transport over complex terrain morphology, varying surface roughness, and a wide range of atmospheric thermal conditions. The surface roughness object of the research is a sparse canopy layer evolving in time along the vegetative season, and characterized by a multiplicity of temporal and spatial scales influencing the properties of the turbulent fluxes. Both experimental and modelling approaches characterize the study methodology. Measurements are first performed in laboratory in order to calibrate flux sensors (i.e., ultrasonic anemometers), and subsequently into three N-W Italy vineyards fields, collecting long term turbulent flux observations over the canopy. Bulk and higher order statistics are explored from these dataset to investigate the turbulent properties of the momentum and heat transfer processes. The analysis is carried out using a conventional quadrant analysis technique and is tested against two models approximating the joint probability density function of the flow variables. Because of direct measurements at field scale are too costly and time consuming, the need to more easily measured parameters for applications in the meteorological and agricultural fields has motivated the examination of a land-surface model, by performing a validation against vineyard data and a sensitivity analysis on canopy parameters. The overall results suggest an improvement procedure for the estimation of turbulent heat flux using sonic anemometers, an insight on the perturbing effect of coherent structures on gradient-diffusion theory, and the key role of canopy parameterizations in the applicative models.

The atmospheric boundary layer in stably-stratified conditions and over non-homogeneous terrain becomes a complex system with many interactions of physical processes occurring in a wide range of different spatial and temporal scales. During clear sky night-time or in any stably-stratified conditions intermittent turbulent events and gravity waves are usually present in the stable boundary layer (SBL), which can substantially modify the flow structure. In addition, the circulations in stable flows can be strongly driven by the underlying and surrounding topography, generating katabatic winds, density currents and low level jets, which in turn, trigger gravity waves and turbulence. This thesis aims to contribute to a better comprehension of some of the processes and phenomena occurring in the SBL and over complex terrain areas. In order to understand and quantify the unknown atmospheric processes one can distinguish three different procedures that are very well connected: theoretical descriptions, experimental campaigns and numerical modeling. The numerical models allow us to further understand the experimental data, to test the theoretical relationships or to simulate processes which are very difficult to measure. Principally, in this thesis we have used numerical models to deal with the uncertainties that arise in stably-stratified flows and over heterogeneous terrain and to explore the model capabilities and limitations to resolve them. These numerical weather prediction models (NWP) contain the primitive equations of the atmosphere to describe and forecast the flow motions and properties. In this thesis we have employed one of the worldwide known NWP model, the Weather Research and Forecasting (WRF) model, using two different approaches: the mesoscale approximation and the large eddy simulation (LES). While the mesoscale methodology has allowed us to investigate the flow circulation patterns in a wide range of scales, the LES approximation has enabled us to explicitly resolve the turbulence and describe its structure. In this thesis each methodology has been applied to investigate these different purposes. Using the WRF model with the mesoscale approach we have determined the origin of a density current that generated internal gravity waves over the "Centro de Investigaciones de la Baja Atmosfera"(CIBA) site. We have seen that the long distance mesoscale sea-breeze circulation and the night-time katabatic flows originated at the surrounding complex topography were the origin of the density current which generated displacement in the air parcels and periodic oscillations. In this thesis we have also investigated the vertical turbulence structure using the LES approximation of the WRF model. As a previous step, we have first validated the WRF-LES model in the SBL with a reference case by a comparison of the first and second order moments profiles. Using different wind speed initial conditions we reproduce neutrally and stably stratified flows. However, different from the reality, stably stratified flows are strongly coupled with the surface and turbulence is always maintained. We have shown how the turbulence intensity increases sharply with the wind speed at each height above ground but the rate of increase (slope) is not maintained, as we would expect. It seems that the the top domain potential temperature inversion affects the flow turbulence structure over the whole domain. Finally, we have studied topographically generated gravity waves over the Pyrenees and specifically simulated a trapped lee wave event using the mesoscale approximation with WRF. We have seen that the model is able to reproduce the gravity waves at the lee side of the mountain range with periodic oscillations in all magnitudes. We have seen that 1-km horizontal resolution is necessary to capture the wave field. We have also showed that upstream conditions have to be well represented to capture the adequate wave characteristics.
La capa límit atmosfèrica és la part més baixa de l'atmosfera terrestre on s'hi desenvolupa la vida humana. En condicions d'estratificació estable i sobre terreny no homogeni esdevé un sistema molt complex amb múltiples interaccions dels processos físics que hi tenen lloc. Per a entendre i quantificar algunes de les incerteses que planteja l'atmosfera a la capa límit en aquesta tesi principalment hem utilitzat eines de simulació numèrica. Els models numèrics permeten la comprensió més enllà de les dades experimentals, així com testejar les descripcions teòriques, a més de simular fenòmens que són molt difícils de mesurar. L'objectiu és, doncs, contribuir a la comprensió dels fenòmens que tenen lloc a la capa límit en condicions d'estratificació estable i sobre àrees de terreny complex i explorar les capacitats i les limitacions de la seva modelització numèrica. D'entre els principals resultats, fent ús del model WRF en l'aproximació de mesoscala, hem determinat l'origen d'una corrent de densitat que va donar lloc a ones de gravetat interna en la zona del Centro de Investigaciones de la Baja Atmósfera (CIBA). Hem vist que una massa d'aire amb origen de brisa marítima juntament amb els vents catabàtics originats a les cadenes muntanyoses del voltant són l'origen de la corrent de densitat que genera ones de gravetat al seu pas per l'àrea del CIBA. Per altra banda, hem explorat l'estructura vertical de la turbulència en condicions neutrals i estables fent ús del model WRF en l'aproximació LES (WRF-LES). S'han investigat els règims de intensitat de turbulència en funció de la velocitat del vent i s'ha obtingut una relació semblant a les observacions en situació de forta turbulència. Veiem les condicions de contorn del model a la superfície i al límit superior poden afectar molt significativament l'estructura dels remolins. Finalment, l'estudi de les ones de muntanya sobre la orografia complexa del Pirineu amb el model WRF en el mode mesoscalar ha permès avaluar la capacitat del model per a representar l'esdeveniment i la variació en els resultats en funció de les seves diferents opcions físiques i de configuració.

[Truncated abstract] The lake boundaries are an important source of sediment, nutrients and chemicals. For life inside the lake, the exchange between the lake boundaries (littoral) and lake interior (pelagic) is of central importance to Limnology as the net flux of nutrients into the water column is both the driving force and limiting factor for most algae blooms found during the stratification period. Consequently, the understanding of the relevant processes defining such an exchange is a further step toward a sound basis for future decisions by lake managers in order to ensure high water quality. The objective of this research was to investigate the physical processes responsible for the exchange of water and particles between the lake boundaries and the lake interior. An integrated approach using field experiments and 3D modelling as applied to Lake Kinneret (Israel) is presented. The field data revealed large-scale metalimnion oscillations with amplitudes up to 10 m in response to westerly diurnal winds, the existence of a well-defined suspended particle intrusion into the metalimnion of the lake, characterized by high concentrations of organic matter, and a well-mixed benthic boundary layer (BBL). The changes in the thermal structure explained the observed vertical and horizontal movements of the suspended particle intrusion. The horizontal advective transport via the metalimnion, associated with the velocities induced by the basin-scale mode-two Poincare wave, controlled the exchange between the lake boundaries and lake interior on daily time scales. The observed BBL over the lake slope varied markedly with time and space. Detailed comparison of simulation results with field data revealed that the model captured the lake hydrodynamics for time scales from hours to days. The model could then be used to extract the residual motions in the various regions of the lake. The residual motions below the surface layer were predominantly forced by the basin-scale internal wave motions, but the residual motion in the surface layer was found to be very sensitive to the curl of the wind field. The residual circulation was responsible for redistributing mass throughout the lake basin on time scales from days to weeks. A clear connection of dynamics of the BBL with the large-scale features of the flow was addressed. The time history of the mixing in the BBL and the resulting cross-shore flux was shown to vary with the phase of the basin-scale internal waves.

Malgré de nombreuses études, le lien de causalité entre vent et vagues fait toujours l’objet de controverses : cela est dû entre autres au caractère multi-échelle d'une surface océanique réaliste, et à la présence de déferlements, qui modifient radicalement sa topologie. Dans cette thèse, ces deux questions sont abordées sous un angle théorique, à travers un modèle phénoménologique, qui relie les propriétés spectrales et moyennées de la turbulence proche de paroi en utilisant la géométrie de tourbillons attachés à celle-ci. La première partie de la thèse revisite ce modèle phénoménologique en questionnant ses hypothèses sous-jacentes et révèle, en particulier, des incohérences dans les modèles utilisés pour décrire le terme de redistribution d'énergie entre composantes turbulentes (modèle de Rotta). Le modèle phénoménologique est ensuite utilisé pour étudier le couplage entre vagues de vent longues (de l'ordre de 10m) et turbulence. Les résultats démontrent que la déformation des tourbillons attachés induite par cette interaction pourrait expliquer une partie de la variabilité des flux de quantité de mouvement à un vent moyen donné. Finalement, le couplage entre la turbulence et les vagues courtes et déferlantes est abordé en définissant une sous-couche rugueuse dans laquelle les propriétés des tourbillons attachés sont définies par la vitesse des fronts déferlants dominants pour un vent donné. Ces deux études posent les bases d'un nouveau paradigme, permettant d'étudier le couplage multi-échelle entre le spectre turbulent et le spectre des vagues. Celui-ci pourrait permettre de mieux prendre en compte l'influence de paramètres environnementaux sur les flux de quantité de mouvement et de chaleur. Il ouvre ainsi de nouvelles perspectives pour les études théoriques et pour l’exploration des données expérimentales
Despite numerous works, the causal link between wind and waves is still a controversial subject. This is due, among others, to the multi-scale nature of a realistic ocean surface and to wave breaking, which changes its topology. In this thesis, such problems are studied from a theoretical perspective, using a phenomenological model linking the spectral and averaged properties of wall-bounded turbulence through the geometry attached eddies.The first part of the thesis revisits this phenomenological model by questioning its underlying assumptions and, in particular, reveals inconsistencies in the models used for the energy redistribution between turbulence components (the Rotta model). The phenomenological model is then used to study the coupling between long wind-waves (of order 10m) and turbulence. Results indicate that the deformation of attached eddies, induced by this interaction, could explain some of the variability in momentum fluxes for a given mean wind. Finally, the study of the coupling between turbulence and short breaking waves is approached by defining a roughness sublayer, in which the properties of the attached eddies depend solely on the speed of the dominant breaking fronts for a given wind. These two studies from the basis of a new paradigm to study the multi-scale coupling between the turbulent and wave spectra. This would allow accounting for the influence of environmental parameters on momentum and heat fluxes, and opens new paths both from a theoretical perspective and for the analysis of experimental data

La modélisation par simulation des grandes échelles (Large-Eddy Simulation - LES) des processus physiques régissant la couche limite atmosphérique (CLA) demeure complexe de part la difficulté des modèles à capter l'évolution de la turbulence entre différentes conditions de stratification. De ce fait, l'étude LES du cycle diurne complet de la CLA comprenant des situations convectives la journée et des conditions stables la nuit est très peu documenté. La simulation de la couche limite stable où la turbulence est faible, intermittente et qui est caractérisée par des structures turbulentes de petite taille est tout particulièrement compliquée. En conséquence, la capacité de la LES à bien reproduire les conditions météorologiques de la CLA, notamment en situation stable, est étudiée à l'aide du code de mécanique des fluides développé par EDF R&D, Code_Saturne. Dans une première étude, le modèle LES est validé sur un cas de couche limite convective quasi stationnaire sur terrain homogène. L'influence des modèles sous-maille de Smagorinsky, Germano-Lilly, Wong-Lilly et WALE (Wall-Adapting Local Eddy-viscosity) ainsi que la sensibilité aux méthodes de paramétrisation sur les champs moyens, les flux et les variances est discutées. Dans une seconde étude le cycle diurne complet de la CLA pendant la campagne de mesure Wangara est modélisé. L'écart aux mesures étant faible le jour, ce travail se concentre sur les difficultés rencontrées la nuit à bien modéliser la couche limite stable. L'impact de différents modèles sous-maille ainsi que la sensibilité au coefficient de Smagorinsky ont été analysés. Par l'intermédiaire d'un couplage radiatif réalisé en LES, les répercussions du rayonnement infrarouge et solaire sur le jet de basse couche nocturne et le gradient thermique près de la surface sont exposées. De plus l'adaptation de la résolution du domaine à l'intensité de la turbulence et la forte stabilité atmosphérique durant l'expérience Wangara sont commentées. Enfin un examen des oscillations numériques inhérentes à Code_Saturne est réalisé afin d'en limiter les effets

The stably stratified nocturnal boundary layer (SBL) can be classified into two distinct regimes: one with moderate to strong winds, weak stratification and mechanically sustained turbulence (wSBL) and the other one with moderate to weak wind conditions, strong stratification and collapsed turbulence (vSBL). With the help of a hidden Markov model (HMM) analysis of the three dimensional state variable space of stratification, mean wind speeds, and wind shear the SBL can be classified in these two regimes in both the Reynolds-averaged as well as turbulence state variables. The two-regime SBL is a generic structure at different tower sites around the world independent of the location specific conditions. Besides clustering the data the HMM analysis calculates the most likely regime occupation sequence which allows for detailed analysis of the structure of the meteorological state variables in conditions of very persistent nights. Conditioning on these very persistent nights clear influences of external drivers (such as pressure gradient force and low level cloud cover) are found. As the HMM analysis captures regime transitions accurately changes of state variables and external drivers across transitions can easily be assessed. Different meteorological state variables behave in times of turbulence collapse (wSBL to vSBL transition) and turbulence recovery (vSBL to wSBL transitions) as expected physically. The results reveal further that clear precursors for transitions in the state variable profiles or external drivers are cannot be determined and that on observed timescales regime transitions are relatively sharp. The absence of clear precursors suggests that parameterisations of SBL regime behaviour and turbulence in the two regimes in weather and climate models have to be stochastic. As regime statistics are relatively insensitive to changes in the stochastic properties of the HMM analysis observed regime statistics are compared to ’freely-running’ Markov chains. The SBL regime statistics do not follow a simple Markov process and more complex parameterisations are necessary. A possible approach of parameterising SBL regime behaviour stochastically using climatological results from this analysis is presented.
Graduate
2019-12-17

The very stable boundary layer is a region of the atmosphere typified by large vertical gradients of temperature and momentum. Analysis of very stable atmospheric flows is complicated by the presence of nonlinear interactions among gravity waves, shear-driven overturning circulations, two-dimensional vortical modes and intermittent turbulence in various stages of development. This study examines the horizontal structure of a very stable atmospheric boundary layer, using data obtained primarily from terrain-following aircraft flights over central Oklahoma. Several diagnostic procedures are applied to the aircraft data, including classical and rotary spectral analysis, principal component analysis, and structure functions. Coherent structures with sharp boundaries are examined with a new conditional sampling technique which requires little a priori specification of sampling criteria. Because the flows involve sharp boundaries, spectral techniques do not provide as much useful information as other more localized procedures. The edges of the coherent structures are regions of significant vertical heat transport, a feature not often emphasized in studies of gravity waves and vortical modes in the stable boundary layer. The presence of significant turbulence even for large stability has implications for modelling of the very stable boundary layer. Forecasts of minimum temperature, boundary layer height, inversion characteristics, and pollutant dispersal are all significantly affected by turbulent mixing. Many models of the stable boundary layer artificially arrest the mixing under stable conditions, resulting in, for example, overestimates of nocturnal cooling. A new parameterization of the stable boundary layer is studied here by incorporating it into an existing model of the planetary boundary layer. The model is then run with one-dimensional sensitivity tests for an idealized atmosphere and with data from Wangara day 33. A simulation over snow cover is also examined. The tests substantiate the role of vertical mixing in ameliorating nocturnal cooling. An additional improvement is a more realistic boundary layer height for moderate wind speeds.
Graduation date: 1988

This thesis investigates several aspects of stratified flow over isolated topography in ocean, lake, and atmospheric settings. Three major sub-topics are addressed: steady, inviscid internal waves trapped over topography in a pycnocline stratification, topographically generated internal waves and their interaction with the viscous bottom boundary layer, and flow over large-scale crater topography in the atmosphere. The first topic examines the conditions that lead to very large internal waves trapped over topography in a fluid with a pycnocline stratification. This type of stratification is connected to ocean or lake settings. The steady-state Euler equations of motion are used to derive a single partial differential equation for the isopycnal displacement in supercritical flows under two conditions: a vertically varying background current under the Boussinesq approximation and a constant background current under non-Boussinesq conditions. A numerical method is developed to solve these equations for an efficient exploration of parameter space. Very large waves are found over depression topography when the background flow speed is close to a limiting value. Variations in the background current are examined, as well as comparisons between Boussinesq and non-Boussinesq results. The second topic aims to extend the above subject by considering unsteady, viscous flows. Once again, supercritical flow over topography in a pycnocline stratification generates internal waves. These internal waves interact with the viscous bottom boundary layer to produce bottom boundary instabilities. The three-dimensional aspects of these instabilities are studied under changes in viscosity. The boundary layer instabilities have important implications for sediment transport in the coastal oceans or lakes. Lastly, the final topic is motivated by the connection between dust streaks on the Martian surface and crater topography. Flow over a large 100-km diameter crater is examined with numerical simulations conducted using the Weather Research and Forecasting model. Modifications to the stratification and topography are applied. It is found that a large hydraulic structure of amplitude comparable to the crater depth forms in many cases. This structure may have important implications for dust transport in the atmosphere. In addition, Martian atmospheric parameters are used to study the flow properties under Mars-like conditions.

碩士
國立高雄海洋科技大學
海洋環境工程研究所
101
VOCs are ozone precursors that contribute to ozone air pollution. The concentration of VOCs may be affected by weather conditions in the atmosphere, which may create stratification. Past literature has proposed that mixing occurs in the inversion layer, leading to the distribution and stratification of VOCs in the atmosphere. However, ozone air quality models have long assumed that the precursor pollutants are uniformly mixed vertically; this may be a source of error for air quality models. In order to confirm that the temperature inversion phenomenon will affect the distribution of VOCs in the atmosphere, this study has monitored the vertical distribution of the concentrations of VOCs in the atmosphere and investigated the correlation with the inversion layer. The study uses the balloon sampling method which measured the temperature and collected air samples from ground level to an elevation of 800 meters and used Entech 7100A thermal desorption by the refrigeration system as pre-handling and GC/MS for the detection of VOCs. Inversion layers occur in the vertical portion of the atmosphere, where it is at a steady and stable state. However, the areas surrounding the inversion layer is not at a stable state. The results of my studies have shown that during the summer, temperature inversion occurs in the morning between 7:00 to 10:00 whereas during the winter, inversion typically occurs between 18:00 to midnight. During these two seasons at 14:00, there is a weak inversion layer near the ground. During inversion, the diffusion of VOCs and air vertically through the atmosphere is very poor. Pollutants that are trapped under the inversion layer cannot disperse into the atmosphere and accumulate near the ground. Above the inversion layer there is pollution caused by long distance transmission and the pollutants become concentrated above the inversion layer. Through POCP and MIR calculations, we found that the formation of the ozone layer will undergo stratification if temperature inversion occurs. Ozone air quality models have long assumed that the precursor pollutants are uniformly mixed vertically; this may be a source of error for AQM. Therefore, we concluded that the vertical atmosphere has an inversion layer that is caused by temperature inversion.

The purpose of this research is the development of a method for studying a two-dimensional semi-linear elliptic partial differential equation in an infinite stripe with slow variations of one of the boundaries. The problem is reformulated as a boundary value problem for a semi-linear elliptic equation with a small parameter at one higher derivative (the singular perturbation parameter). The method is based on the boundary function of Tikhonov, shaped by Vasil?eva and Butuzov for a one-dimensional case. The developed method has clear parallels with the one-dimensional boundary function method.

Little work has been done to estimate turbulence characteristics in the hypolimnetic waters of large lakes, where the magnitude and vertical structure of turbulent parameters have important implications for nutrient cycling and benthic exchange. In this thesis, hypolimnetic mixing is investigated over the annual stratification cycle in a large lake using a series of experiments in Lake Michigan that utilize acoustic Doppler velocimeters, thermistors, and microstructure profilers to characterize mean flow and turbulence throughout the water column. More than 500 days of physical limnological data were collected and analyzed over the course of this study, creating the most comprehensive data set of its kind in the Laurentian Great Lakes. While we found that bottom boundary layer turbulence and mean flow follow law-of-the-wall predictions in the mean, individual estimates were shown to deviate significantly from canonical expectations, with deviations linked to weakly energetic flow conditions (i.e. low speeds) and seiche-scale flow unsteadiness. Bottom boundary layer characteristics, including the mean current speed (U₅₀=3 cm/s), drag coefficient (Cd₅₀=0.0052), and turbulent kinetic energy dissipation (ϵ₅₀ =10^-8 W/kg), showed very little seasonal variation, despite highly variable surface forcing (e.g. stratification, wind speeds). Full water column turbulence profiles measured during the stratified summer were largely buoyancy suppressed, with internal Poincaré waves driving enhanced turbulent kinetic energy dissipation (ϵ= 10^-7 W/kg) in the relatively compact thermocline and weak hypolimnetic mixing (turbulent scalar diffusivity: K_z=10^-6 m²/s) limiting benthic nutrient delivery. Although small temperature gradients drove strong mixing over the isothermal period (K_z=10^-3 m²/s), velocity shear was overwhelmed by weakly stable stratification (Richardson number:Ri≈0.2), limiting the development of the surface mixed layer and suppressing hypolimnetic turbulence (ϵ=10^-9 W/kg; K_z=10^-4 m²/s). When surface temperatures fell below the temperature of maximum density (T_MD≈ 4℃), radiative convection played a major role in driving vertical transport, with energetic full water column mixing throughout the day followed by surface cooling and restratification overnight. During this “convective winter” period, daily temperature instabilities were directly correlated with elevated turbulence levels (ϵ=10^-7 W/kg; K_z≈10^-1 m²/s), and overnight turbulence characteristics were similar to those observed over the isothermal spring. Near surface dissipation and diffusivity measurements followed similarity scaling arguments, with wind shear and surface fluxes dominating production in the surface mixed layer during all three seasons. Together, these results are used to model the influence of invasive dreissenids over each forcing period, providing insight into the annual variability of effective filtration rates in the calm, hypolimnetic waters of Lake Michigan.

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.

The motion of buoyancy driven plumes is, on all scales, the most common heat and momentum transfer mechanism in geophysical flows, well known as Free Convection. Similarly, density stratification due to heating inequalities is also an ordinary scenario in nature. Free Convection phenomenon coupled with a density stratified fluid setting leads to the so-called Penetrative Free Convection (PFC). When a fluid, in static equilibrium, is stably stratified a thermal forcing can produce an unstable configuration ensuing internal waves formation of increasing amplitude. If the perturbation is strong enough, it can definitely erode the initial stratification and cause the motion of turbulent buoyant updrafts, dome-shaped, compensated by denser downdrafts. The entrainment phenomenon occurring at the interface between the turbulent and non-turbulent region justifies the penetrative feature of convection and causes the non linear growth of the Convective Boundary Layer (CBL) of well mixed fluid against the adjacent stably stratified region. In addition to the wide engineering applications, the environmental impact mostly motivates PFC studies. The upper lakes and oceans, under calm conditions, usually exhibit a continuous, moderately stable density distribution. Turbulent convective flow can be generated both by the free-surface cooling and wind shear-stress, eroding the stable stratification on a daily or seasonal time scale. Domes with large downward velocities are generated at the free surface, balanced by updrafts with lower velocity but larger area. Because of the relatively rapid mixing, the density distribution is approximately uniform in the upper layer and it deepens with time as a result of the entrainment and erosion of the underlying denser water. An analogous phenomenon is observed in the lower troposphere when surface heating due to solar radiation results in a growing unstable layer adjacent to the ground which replaces a nocturnal inversion from below. In this case, the initially stable environment near the ground is affected by convection characterized by relatively narrow and fast plumes of rising horizontal surfaces balanced by larger regions of downward slower motion. Resulting internal waves generated within the stable layer take place at or below the Brunt-Väisälä frequency, which is related to the vertical temperature gradient. In nature, the dynamics of the CBL influences the transport and mixing features of a given stratified fluid-body. The amount of materials being mixed due to penetrative convection is a crucial issue both in water or air quality monitoring and forecast with important implications in environmentally-friendly studies. Focusing on the environmental aspect, the pollutant dispersion is a matter of particular importance. On one hand, mixing processes inside the CBL help increasing dispersion with some positive consequences: the concentration of potential harmful pollutants in high risk zones tends to decrease, the turnover and the redistribution of vital substances, like oxygen and nutrients, is guaranteed; the latter plays a major role in large water bodies. These advantages are essential for the safety of populations living close to urban or industrial areas, or for preserving coastal human activities and ecosystems. On the other hand each pollutant, released inside the CBL mainly by human activities, remains confined inside it because of the interface with the non-turbulent region, which acts as a barrier for outward transport. Considering the proximity of the CBL with biosphere, a deeper insight into dispersion and entrainment processes appears mandatory either for sustainable engineering design or for monitoring purposes. Given the great applicability of the topic in several scientific and engineering fields, large amount of experimental, theoretical and numerical investigations on CBL development in a continuously and linearly stratified fluid setting had been conducted in the past since sixties. It appears there is a lack of consensus about the dependence of integral parameters of convective entrainment (in particular the CBL growth rate) on the initial stratification strength and convective phenomenon evolution. Driven by all these premises the main aims of the present research are related to better understanding dispersion of a passive scalar inside the CBL with a lagrangian, non-local approach and a fully three-dimensional (3D 3C) experimental technique, which for the first time has been applied to the topic. When turbulent convection occurs, in fact, dispersion is mostly due to transport by large organized structures while molecular diffusion can be neglected. Given this assumption, a non local approach based on a fully advective-like behaviour of the tracer is necessary and a lagrangian description of flow may be more suitable. Moreover, the knowledge of the horizontal and vertical extension of the structures dominating the flow field appears to be mandatory. Furthermore, turbulence is fully three-dimensional on the scales of motion characterising the phenomena in nature. In order to better understanding and likely describing the evolution of turbulent structures inside the convective layer, a three dimensional experimental technique is strongly required. In the present work shear free convection experiments in a stably stratified environment were performed in a thermally controlled convection chamber. The experimental set up was arranged in different optical configurations to ensure the two components and three components of velocity to be measured in an illuminated plane and volume respectively through different image analysis techniques with sub-pixel accuracy. Temperature measurements were simultaneously acquired using thermocouples of accuracy less than 0.1 °C. The experiments highlighted the time evolution of the convective structure characteristic spatial scales (CBL height and horizontal spacing between thermals) and the non local description of transport and mixing inside the growing CBL. The main novelty of the present contribution covers the improvement of techniques and methods to achieve more reliable, statistically robust and likely results. The experimental effort based on image analysis techniques (mainly Feature Tracking and photogrammetric 3D-PTV) resulted suitable for reconstructing longer trajectories (always more than 103 trajectories longer than 20 consecutive snapshots) and analyzing larger particle density images (reliable results for more than 2000 particles in a volume of 15X15X15 cm3 for 3D-PTV). Velocity statistics are then more robust than those from classical Particle Tracking Velocimetry. Moreover, for the first time, a fully three-dimensional particle tracking technique has been applied to penetrative convection experiments. 3D-PTV allows a more realistic description of the velocity field, which occurs during the evolution of the convective mixed layer, than more traditional 2D techniques. Furthermore, photogrammetric 3D-PTV rather than “scanning” 3D-PTV results in more accuracy when the tracer particle density is high, because particles may be tracked directly in the 3D space rather than through matching of 2D projections. The broader impact of the research mainly refers to the prediction of the CBL growth as a function of initial and boundary conditions with better accuracy than conventional and well established techniques. The experimental study can thus give a positive contribution on real pollutant dispersion studies in urban and natural environments for environmental protection and sustainable design purposes. Field experiments aimed at measuring the turbulence budget of the CBL have shown that the mechanical generation of kinetic energy by wind shear is often confined close to the heat source supporting the validity of laboratory models in which no wind is present. According to this assumption, the similarity proposed by Deardorff (1970) is employed to compute scaling parameters and to make results comparable with real scales. Through normalizing the quantities measured at different stages of the experiment, the phenomenon can be considered as a succession of steady states, according to an evolution of the variables of interest that may be defined quasi-steady state. The experimental apparatus employed to run the experiments is the same as in Cenedese and Querzoli (1994), Querzoli (1996), Cenedese and Querzoli (1997) and Moroni and Cenedese (2006). The spatial resolution of velocity data is largely increased here by means of 2D and 3D image analysis techniques (Feature Tracking, FT, and 3D Particle Tracking Velocimetry, 3D-PTV) used instead of Laser-Doppler Anemometry or 2D Particle Tracking Velocimetry as in Cenedese and Querzoli, 1994; Querzoli, 1996 and Cenedese and Querzoli, 1997. Moreover the photogrammetric 3D-PTV here applied allows fully three-dimensional descriptions of both the Eulerian velocity field and Lagrangian particle trajectories for a more likely understanding of the phenomenon than through the 2D approach used in Moroni and Cenedese (2006). Furthermore, the combined use of thermocouples and flow visualization techniques allows cross-validating different methods to estimate the evolutions of the key parameters and the plume characteristic dimensions. Two different experimental arrangements were set-up, 2D and a 3D models. A large set of data were firstly acquired using a 2D model and employing FT. The preliminary investigation was mainly focused on better understanding the physics of the phenomenon, finding a time scaling law, testing different methods to compute the variables of interest and comparing results with classical methods found in literature. When 2D techniques are employed to detect the velocity field, the flow is illuminated with a thin light sheet and only the velocity components within this sheet can be evaluated. Driven by the idea that only a fully three-dimensional technique can significantly improve our laboratory model in term of a more likely description of free convection structures we run a second set of experiments, by using a stereoscopic arrangement of cameras focused on an illuminated volume. Although some methods do exist for reconstructing 3D velocities in a point (3D laser Doppler Anemometry; Hinsch and Hinrichs, 1996) or plane (3D stereo-PIV; Stuer et al., 1999), only a fully 3D technique based on the illumination of a flow volume rather than a flow sheet will give the information needed to construct the instantaneous 3D velocity fields. A number of imaging-based measurement techniques exist for determining 3D velocity fields in an observation volume. Among these are: scanning, photogrammetric, holographic or photogrammetric techniques dependending on which principle is recalled to reconstruct the third dimension from a 2D image/s: The present study was focused on 3D-PTV which is a 3D extension of the 2D particle-tracking methods. 3D-PTV is based on reconstructing 3D trajectories of reflecting tracer particles through a photogrammetric recording of image sequences. The 3D particle trajectories obtained can be used to calculate the 3D velocity field. The 3D-PTV optical system has been designed with the following capabilities: image a volume far away the boundary walls, lengthen the trajectories, and improve the accuracy of the procedure through a careful test on synthetically generated data. A physically-based photogrammetric calibration of the stereoscopic arrangement was employed and its accuracy tested. The effects of multimedia geometry on calibration parameters were taken into account. The combination of image- and object-space based information was employed to establish the correspondences between particle positions (structure from stereo reconstruction). A particle tracking algorithm was then employed to reconstructed 3D trajectories. Sensitivity tests conducted on the matching algorithm proved that the calibration accuracy is fundamental to obtain the correct matching and particle tracking; small errors in calibration parameters or neglecting water refraction effects reduce matching performance. On the other hand, accuracy less than 1 pixel was reached with our calibration procedure ensuring good results in the matching procedure. Tests on synthetic data demonstrated a multi-choice strategy with a 3 camera arrangement is the best solution for matching data. It is less sensitive to errors in the calibration data set when both the percentage of correctly matched triplets and the number of outputs of the algorithm were considered. Original and cross-validating methods to compute the CBL height and horizontal scale of thermals were applied based on temperature, velocity and fluorescence imaging. The spatial covariance of the velocity field, providing the plume horizontal spacing, allows the spatial extension of the mixed region to be determined. Dome characteristic vertical dimension is of the same order of magnitude as the mixing layer height, while their horizontal dimension becomes similar to the vertical one at the end of the experiment when the structure dimensions are comparable to the test section side and border effects are no longer negligible. The mixing layer growth was computed by exploiting both temperature and velocity data. Outputs were then compared to more classical methods as the zero-order mixed-layer model and the zero-heat flux level method. The accuracy of our methods was computed as well. Present results, normalized accordingly to the Deardorff similarity for free convection, were compared with literature data and LES meteorological models. Outcomes from different experimental configurations, literature and LES models are in fairly good agreement. The comparison with literature data at real scale demonstrates the validity of our experimental task and its applicability for the study of the real atmospheric boundary layer and its monitoring for environmental purposes. On the other hand the agreement with LES models at different boundary conditions and domain aspect ratios proves that both scale and border effects of the experimental model are negligible if data are not processed for too long time.