This report presents the study of two-equation turbulence modeling. The primary objective of this study is to implement two-equation k-ε and k-ω turbulence models as a part of the incompressible flow solver, U²NCLE, on unstructured grids. There are several two-equation models but the selection of one which is in par with the model in UNCLE solver is required so that this model can be compared for robustness and accuracy as dem-onstrated by turbulence models in UNCLE. The selection also requires that the pre-defined arrays and variables can be used to avoid overhead and deviation from the solution procedure used in U²NCLE. The present study deals with the two-equation k-ε model contributed by Shih and Lumley and the two-equation k-ω model contributed by Wilcox. Implementation of these models will give the user multiple options of two-equation turbulence modeling for solution purpose. Particular attention is paid to the efficiency of the implementation. Various approximations to the source terms are considered and the most optimal and accurate approximation is identified. These models are validated via relatively small model problems, for example a flat plate case, by comparing the results with the results obtained from the respective models in UNCLE and the existing two-equation q-ω model in U²NCLE. Further validation is carried out by comparing computed forces and moments with experi-mental data for the SUBOFF model with sail and stern appendages.

No description available.

Thesis (Ph. D.)--University of Canterbury, 2009. / Typescript (photocopy). "November 24, 2009." Includes bibliographical references (p. 325-330). Also available via the World Wide Web.

In this PhD Thesis, we have studied several problems related to statistical properties of homogeneous, isotropic and turbulent flow of conducting fluid with direct numerical simulations (DNS) of equations of magnetohydrodynamics (MHD) and simplified shell models. The Thesis begins with an introductory overview of several statistical characterisation of fluid turbulence and MHD turbulence. Chapter-1 discusses various challenges in turbulence in MHD context. This chapter also describes specific problems that are attempted in this Thesis. The first problem, contained in Chapter 2, deals with dynamo action in a shell model for magnetohydrodynamic (MHD) turbulence. We have carried out systematic and high-resolution studies of dynamo action in a shell model over a wide range of the magnetic Prandtl number PrMand the magnetic Reynolds number ReM. Our study suggests that it is natural to think of dynamo onset as a nonequilibrium, first-order phase transition between two different turbulent, but statistically steady, states. The ratio of the magnetic and kinetic energies is a convenient order parameter for this transition. By using this order parameter, we obtain the stability diagram (or nonequilibrium phase diagram) for dynamo formation in our MHD shell model in the (PrM−1,ReM)plane. The dynamo boundary, which separates dynamo and no-dynamo regions, appears to have a fractal character. We obtain hysteretic behavior of the order parameter across this boundary and suggestions of nucleation-type phenomena. In Chapter 3 we present the results of our detailed pseudospectral direct numerical simulation (DNS) studies, with up to 10243 collocation points, of in-compressible, magnetohydrodynamic (MHD) turbulence in three dimensions, without a mean magnetic field. Our study concentrates on the dependence of various statistical properties of both decaying and statistically steady MHD turbulence on the magnetic Prandtl number PrMover a large range, namely, 0.01 ≤PrM≤10. We obtain data for a wide variety of statistical measures such as probability distribution functions (PDFs) of moduli of the vorticity and current density, the energy dissipation rates, and velocity and magnetic-field increments, energy and other spectra, velocity and magnetic-field structure func-tions, which we use to characterise intermittency, isosurfaces of quantities such as the moduli of the vorticity and current, and joint PDFs such as those of fluid and magnetic dissipation rates. Our systematic study uncovers in-teresting results that have not been noted hitherto. In particular, we find a crossover from larger intermittency in the magnetic field than in the velocity field, at large PrM, to smaller intermittency in the magnetic field than in the velocity field, at low PrM. Furthermore, a comparison of our results for decaying MHD turbulence and its forced, statistically steady analogue suggests that we have strong universality in the sense that, for a fixed value of PrM, multi-scaling exponent ratios agree, at least within our error bars, for both decaying and statistically steady homogeneous, isotropic MHD turbulence. Chapter 4 is devoted to pseudospectral direct numerical simulation (DNS) studies of the three-dimensional magnetohydrodynamic (MHD) equations (3DRFMHD) stirred by a stochastic force with zero mean and a variance ∼ k−3, where kis the wavevector, for magnetic Prandtl numbers PrM=0.1,1, and 10. We obtain velocity and magnetic-field structure functions and, from these, the multiscaling exponent ratios ζp/ζ3by using the extended self similarity (ESS) procedure. These exponent ratios lie within error bars of their counterparts for conventional three-dimensinal MHD turbulence (3DMHD). We carry out a systematic comparison of the statistical properties of 3DMHD and 3DRFMHD turbulence by examining various probability distribution functions (PDFs), joint PDFs, and isosurfaces of quantities such as the moduli of the vorticity and the cur-rent density. In Chapter 5 we present a study of the multiscaling of time-depedent velocity and magnetic-field structure functions in homogeneous, isotropic fluid turbulence. We first present a generalisation for magnetohydrodynamics of the formalisn that has been developed for analogous studies of time-dependent structure functions in fluid turbulence. We then carry out a detailed numerical study of such time-dependent structure functions in a shell model for MHD turbulence. From this study we extract both eqaul-time and dynamic multiscaling exponents; however, we have not so far been able to come up with the MHD analogues of the linear bridge relations that relate equal-time and dynamic multiscaling exponents in fluid turbulence; indeed, it is not clear whether such bridge relations should exist for MHD turbulence.

La turbulence d'onde faible (TTF) est une théorie statistique appliquée à un ensemble d'ondes aléatoires non cohérentes et dispersives. En supposant un domaine infini et une nonlinéarité infinitésimale, une prédiction sur la cascade d'énergie entre échelles par le biais d'interactions résonantes des échelles d'injection aux échelles dissipatives est alors possible. La théorie semble souvent mise en défaut par la confrontation expérimentale pour les ondes de surface. Une explication potentielle de cette divergence entre expérience et théorie est l'aspect fortement restrictif des hypothèses nécessaires à la validité de la théorie. Nous proposons dans cette thèse d'explorer l'impact du non-respect de certaines de ces hypothèses sur les propriétés statistiques de la turbulence. Des expériences à l'interface de deux liquides non-miscibles ont été entreprises afin d'étudier l'impact de l'augmentation de la dissipation visqueuse et donc de la réduction du temps dissipatif sur la mise en place de la cascade d'énergie. Une expérience à la surface de l'eau avec un confinement progressif de la largeur de la cuve a été effectuée afin d'observer une potentielle coexistence de la turbulence discrète, dans la direction confinée, et continue, dans la direction non confinée. Une analyse expérimentale des ondes gravito-capillaires où la dispersion a été réduite a permis de mettre en lumière une transition d'un régime de TTF vers un régime contenant des structures cohérentes localisées que sont les solitons. Afin de vérifier si une telle transition peut être visible sur un système physique différent, une étude expérimentale et numérique ont été conduites sur les ondes dans une plaque élastique précontrainte. Dans ce milieu l'effet de dispersion des ondes de flexion et en compétition avec le caractère non-dispersif des ondes de tension. Nous nous intéresserons par ailleurs numériquement aux régimes faiblement et fortement non-linéaires des ondes purement non-dispersives dans la membrane. / Weak wave turbulence (WTT) is a statistical theory applied to a large number of incoherent and dispersive waves. Based on the hypothesis of small non-linearity and infinite domain the theory predicts an energy cascade from the forcing scales to the dissipative scales. The confrontation of WTT to experiment for surface waves raises many inconsistencies. The strong hypotheses on which is developed the WWT may be the explanation of such disparity between experiment and theory. The aim of this Thesis is to investigate the impact of the invalidation of some of these conditions on the statistical properties of turbulence. Experiments of interfacial waves between two non-miscible fluids with different viscosities have been carried out to characterize the effect of the increase of viscous dissipation on the energy cascade. An experiment at the surface of water with an increasing confinement of the width of the vessel has been done in order to possibly observe a co-existence between discrete turbulence and classical turbulence. An experimental study of gravity-capillary waves with a decrease of dispersion led us to the observation of a transition to a solitonic regime. In order to verify whether such a transition can be observed in a different physical system, an experimental and numerical study were conducted on the waves in a prestressed elastic plate. In this medium, the effect of dispersion of bending waves is competing with the non-dispersive aspect of stretching waves. We also studied weakly and strongly non-linear regimes of purely stretching waves in a membrane.

At high winds, turbulence in the ocean surface mixed layer is dominated by organized coherent structures in the form of counterrotating helical vortices known as Langmuir cells. While the dynamics of the ocean surface layer has been studied rather extensively at lower wind speeds, the detailed physics at higher winds has remained largely inaccessible because of limited sea-going operations and difficulty conducting in situ measurements at high sea states. In the present thesis new measurement techniques, based on acoustical remote sensing, are described. A freely drifting imaging sonar was employed, which allowed us to follow time-evolving features for an extended period of time. This imaging sonar extends the acoustical approach beyond fixed orientation sonars and covers a full 360° circle on the surface. The full circle capability turns out to be a key addition to the measurements: it allowed quantitative evaluation of the directional properties of Langmuir circulation surface structure. These new methods allow us to sample near-surface circulation and bubble distributions even in extreme conditions, and contribute to our understanding of small scale dynamics in the wind driven surface layer. Using vertical velocity measurements in the convergent regions of Langmuir circulation and a model scaling, we infer the effective viscosity relevant to cell generation. Matching velocity- and temperature-inferred turbulent viscosities we estimate the depth scale over which the wind-wave forcing is of most importance. The velocity-inferred viscosity compares favorably with the mean model viscosity values evaluated at approximately two significant wave heights below the surface. Combining the effective viscosity calculated at different depths with the observed Stokes drift and friction velocity we estimate Langmuir numbers La between 0.015 and 0.1. We observe evolving cell patterns at larger La (between 0.02 and 0.05), which indicates that higher viscosity values than previously assumed in the models may be relevant for Langmuir circulation dynamics. Acoustical observations of the orientation of surface bubble clouds and the directional wave field during several deployments provided an opportunity for comparison of the directional properties of Langmuir circulation with a model that takes into account effects associated with misalignment of the Stokes drift and wind forcing. Model results imply that the growth rate is maximal overall when wind and waves are aligned. For a given angle between the Stokes drift and the wind (the misalignment angle) the direction of the cell axis for maximal growth lies between the Stokes drift and the wind and is mainly determined by (i) the misalignment angle and (ii) the ratio of the Stokes drift shear and mean Eulerian shear. Our ocean observations showed Langmuir cells responding to the changes in wind direction within 15 to 20 min. On two occasions, when the wind changed direction and waves lagged behind, the cells were observed to form in an intermediate direction (between wind and waves) consistent with model predictions. Observations of the near-surface circulation and thermal structure during a storm motivate analysis in terms of the Froude number derived from the measured vertical density gradient, the turbulent diffusivity which is inferred from the measured temperature distributions, and velocity and spatial structure of the circulation. The results demonstrate inhibition of Langmuir circulation by the presence of warm surface water at the beginning of a storm and provide a test of model description of the balance between wind-driven stirring and buoyant resistance. To better understand our measurements and the limitations of the approach, based on the acoustical backscatter, a technique for scatter location estimation is proposed. By comparing velocity magnitudes, independently measured with side-looking and upward-looking sonars, we estimate an effective scattering depth. These results show that the backscatter measured with side-looking sonars originates not right at the surface but at some depth below. / Graduate

Les vagues et les ondes internes de gravité ont un impact important surl’hydrodynamique et l’hydrologie de la zone côtière. Les vagues extrêmes sontparticulièrement intéressantes à étudier, car elles sont une menace sérieuse pour letransport maritime, les plates-formes pétrolières, les installations portuaires et leszones touristiques de la côte. Ces ondes entravent aussi les activités humainesdéveloppées à la côte. Les ondes internes non linéaires affectent la biosphèreaquatique, notamment le transport de sédiments et créent des affouillements à labase des plates-formes et des pipelines. Elles affectent également la propagationdes signaux acoustiques. Les vagues scélérates provoquent d’importants dégâtsmatériels et de nombreuses pertes en vies humaines. Par conséquent, l’étude de laformation des ondes scélérates dans la zone côtière est d’une importance capitale.L'objectif principal de la thèse est l'étude de la formation d’ondes océaniquesanormales dans la zone côtières pour différentes profondeurs d’eau et différentschamps d'ondes. Il est montré que le mécanisme de focalisation dispersive àl’origine de la formation d’ondes scélérates est pertinent quand les ondesinteragissent avec une paroi verticale. Il est démontré que juste avant la formationde l’onde maximale, celle-ci change rapidement de forme, d'une haute crête vers uncreux profond. La durée de vie de l’onde scélérate augmente avec le nombred’ondes individuelles contenues dans le paquet d'ondes anormales et lorsque laprofondeur de l'eau diminue.Il est démontré que l'interaction de paires de solitons unipolaires conduit à unediminution des facteurs de dissymétrie et d’aplatissement du champ d'ondes. Il estprouvé que dans le cas d'interactions hétéropolaires de solitons, le facteurd’aplatissement augmente.La dynamique non linéaire de champs de solitons unipolaires aléatoires estétudiée dans le cadre de l’équation de Korteweg - de Vries (KdV) et de l’équationde Korteweg - de Vries modifiée (mKdV). Il est montré que les coefficients dedissymétrie et d'aplatissement du gaz de solitons sont réduits à la suite de collisionsde solitons. Les fonctions de distribution des amplitudes des ondes sont obtenues.Le comportement des champs solitoniques dans le cadre de ces modèles estqualitativement similaire. Il est démontré que l'amplitude des ondes extrêmesdiminue en moyenne en raison des interactions entre multi-solitons.Dans le cadre de l'équation de Korteweg-de Vries modifiée, les interactionsnon linéaires entre le soliton de plus petite amplitude et les autres solitons du gazont pour effet de réduire sa célérité qui devient négative et de modifier ainsi sadirection de propagation.A partir de l'équation de Korteweg-de Vries modifiée, il est prouvé que dans ungaz de solitons héteropolaires, des ondes scélérates peuvent se former. Laprobabilité d’occurrence et l’amplitude des ondes scélérates dans de tels systèmesaugmente avec la densité du gaz de solitons. / Surface and internal gravity waves have an important impact on the hydrological regime ofthe coastal zone. Intensive surface waves are particularly interesting to study because they canbe a serious threat to ships, oil platforms, port facilities and tourist areas on the coast; suchwaves hampered the implementation of human activities on the shelf. Nonlinear internal wavesaffect the underwater biosphere and cause sediment transport, they create washouts soil at thebase of platforms and pipelines, affect the propagation of acoustic signals. Freak waves have aparticularly strong impact, and they are studied in this thesis. Therefore, the study of freak waveformation in the coastal zone is relevant and practically significant.The main goal of the thesis is the study of particularities of abnormal wave formation incoastal zones under different assumptions on the water depth and wave field form. In particular,it is demonstrated that the mechanism of dispersion focusing of freak wave formation "works"for waves interacting with a vertical barrier. It is shown that just before the maximum waveformation a freak wave quickly changes its shape from a high ridge to a deep depression.Lifetime of freak wave increases with the growth of number of individual waves in anomalouswave packet, and lifetime of freak wave increases with water depth decreasing.It is demonstrated that pair interaction of unipolar solitons leads to decrease of the thirdand fourth moments of the wave field. It is shown that in the case of heteropolar solitoninteraction the fourth moment increases.The nonlinear dynamics of ensembles of random unipolar solitons in the framework of theKorteweg - de Vries equation and the modified Korteweg - de Vries equation is studied. It isshown that the coefficients of skewness and kurtosis of the soliton gas are reduced as a resultof soliton collision, the distribution function of wave amplitudes are defined. The behavior ofsoliton fields in the framework of these models is qualitatively similar. It is shown that in thesefields the amplitude of the big waves is decreased in average due to multi-soliton interactions.A new braking effect of soliton with a small amplitude and even changing of its direction inmulti-soliton gas as a result of nonlinear interaction with other solitons is found in the frameworkof the modified Korteweg-de Vries equation.It is shown that in heteropolar soliton gas abnormally big waves (freak waves) appear inthe frameworks of the modified Korteweg - de Vries equation. With increasing of soliton gasdensity the probability and intensity of freak waves in such systems increases.

Les recherches en milieu lacustre ont généralement porté sur les grands lacs naturels et les barrages. Or les défis scientifiques que présentent les lacs urbains sont nombreux du fait de leur faible profondeur et de leur extension .Le travail que nous présentons ici s'inscrit dans le cadre du projet Petits Lacs Urbains Mesures Modèles Multi-Echelles (PLUMMME), projet financé par la région Île-de-France (programme DIM R2DS).Ce projet a permis l'équipement du lac de Créteil en mesures à haute résolution. Ce sont ces mesures physiques et biologiques qui sont essentiellement exploitées dans cette thèse, parfois en comparaison avec celles du lac du Bourget. La première étape de cette thèse a été ainsi d'enrichir la base de données déjà disponible. Pour cela, nous avons mis en place une station de mesure en continu (capteurs de température, chlorophylle et luminosité, données météorologique telles que vitesse du vent et température atmosphérique), ainsi que deux chaînes de mesures comportant différents capteurs. Des campagnes de mesures spécifiques ont également été réalisées pour l'étude de hydrodynamique à l'aide d'un courantomètre de type Acoustic Doppler Velocimeter (ADV), ainsi qu'un profileur de type Acoustic Doppler Current Profilers (ADCP) à deux points différents du lac (point central et point du rejet d'eaux pluviales). L'analyse des différents champs montre que le lac présente des stratifications avec une période d'une semaine. Nous avons également identifié les modes d'oscillations des ondes internes lorsque ces dernières se produisent sous l'effet du vent. L'analyse spectrale a permis de mettre en évidence une première propriété d'invariance d'échelle des différents champs mesurés. Les différents processus physique (turbulence, stratification, écoulement proche de la paroi) opérant le long de la colonne d'eau ont également été caractérisés. L'analyse spectrale ne permet pas de mettre en évidence le caractère intermittent des fluctuations des champs mesurés, ces dernières peuvent par contre être analysées à l'aide des techniques multifractales. Dans cette thèse nous avons montré que lorsqu'il existe une dépendance entre deux champs, celle ci est multi-échelle. L'utilisation du modèle multifractal universel (UM) a permis de quantifier le degré de cette dépendance. La qualité de l'estimation des paramètres UM dépend fortement de celle de l'invariance d'échelle observée: des séries temporelles présentant des tendances ne respectent pas cette invariance. Les effets de ces dernières sur l'estimation des paramètres UM peuvent être éliminés en utilisant la méthode de décomposition empirique modale dans l'espace physique. L'utilisation des données du champ de vitesse mesuré à l'aide de l'ADCP montre que, les pentes des spectres suivent un profil logarithmique selon la verticale, cela met en évidence que différents processus physiques opèrent le long de la colonne d'eau. Nous montrons également que l'hydrodynamique du lac est fortement perturbée à petite échelle au point du rejet d'eau pluviale. La dernière partie de la thèse examine ce que notre analyse à petites échelles apporte aux modèles numériques. Nous montrons que si les modèles déterministes arrivent à reproduire certains phénomènes à grande échelle, ils sont dans l'incapacité de représenter correctement les fluctuations à petites échelles, donc les processus physiques correspondants. L'analyse multifractale montre que la variabilité des champs physiques présente une forte intermittence. Le fait que la majorité des interactions biologiques/chimiques se produisent à petites échelles souligne la nécessité d'améliorer qualitativement les modèles de fermeture des équations de Navier-Stokes. Enfin, nous montrons que les fonctions de structures, observables statistiques de base en turbulence, ne permettent pas de caractériser de façon unique les champs non conservatifs et donc correspondent à des simulations multifractales non identiques / Research in limnology has generally focused on natural lakes and dams. Moreover, the scientific challenges posed by urban lakes are numerous because of their large width and shallow depth resulting in complex problems that involve. This work is part of the project Petits Lacs Urbains Mesures Modèles Multi-Echelles (PLUMMME), founded by Région Île-de-France (DIM R2DS program). The project provides the high-resolution equipment measuring equipment used at Lake Créteil. Physical and biological measurements are the primary scope of this thesis, with some comparisons of measurements done between Lake Creteil and Lake Bourget. With this in mind, the first step of the thesis was to enhance currently available data. In order to do this we installed a station for the continuous measurement of: temperature, chlorophyll and light, also meteorological quantities such as wind speed, and air temperature were measured. The quantities were measured using two measuring chains comprising different sensors. Measurements were conducted in order to characterise hydrodynamics, using a current meter of type Acoustic Doppler Velocimeter (ADV) and a profiler of type Acoustic Doppler Current Profilers (ADCP) positioned at different points in the lake (centrally, and at the point of stormwater discharge). The analysis of the various measured fields shows that the lake is periodically stratified with a period of one week. We also identify the different modes of the internal waves that occur due to the effects of the wind. Spectral analysis was used to highlight the first scale invariant propriety of the different measured fields. Various physical processes (turbulence, stratification, near-wall flow) operating along the water column were also characterised using this method. The spectral analysis, however, does not provide information about the intermittency of the fluctuations of the measured fields, this can only be done using multifractal techniques. In this thesis, we have shown that when there is a dependence between two fields, the dependence is multiscale. The use of the Universal Multifractal (UM) model, allows one to quantify the degree of this dependence. The quality of the estimation of the UM parameters depends strongly on that of the observed scale: time-series with trends are not scaling. The effects of the latter on the estimation of UM parameters can be improved by the application of the Empirical Modal Decomposition method. The measured velocity data from the ADCP shows that the slope of the power spectra density follow a logarithmic profile along the depth of the lake, it shows that different physical processes operate along the water column. We also show that the hydrodynamics of the lake at small scale are strongly perturbed at the point of waterstorm discharge. The last part of the thesis is focused on what our analysis at small-scales brings to numerical models. We show that, if the deterministic models are able to reproduce some phenomena at large scale, they fail to describe the small-scale variability. the small scale variability and the physical processes involved. A multifractal analysis showed that the small-scale variability of the physical fields displays a strong intermittency, an extremely important feature for biological or chemical reactions and therefore for biological scenarios. Knowing that the majority of biological/chemical interactions occur at smaller scales, this result underlines the necessity to greatly improve the closure of the Navier-Stokes equations. Finally, we show that the structure function, a frequently used statistical tool in turbulence, do not uniquely characterize non-conservative fields, i.e., they do not correspond to identical simulations

No description available.

No description available.