Depuis les travaux pionniers de Brown et Roshko portant sur les effets des variations de masse volumique au sein de l’écoulement de couche de mélange, plusieurs autres études tant théoriques, expérimentales ou numériques se sont attelées à étudier finement cet écoulement. Les motivations sont d’ordre pratiques (industrie de la chimie, l’aérodynamique, la combustion . . .) ou alors purement théoriques (rôle des structures cohérentes, instabilités secondaires. . .). Ces études se sont intéressées, entre autres, aux effets de compressibilité et/ou de masse volumique variable. A notre connaissance, les effets des variations de viscosité dans la configuration de couche de mélange sont peu abordés dans la littérature. L’objectif de ces travaux de recherche est l’exploration théorique et numérique de l’écoulement de couche de mélange temporelle à viscosité variable, plus particulièrement durant sa phase initiale de développement. D’un point de vu numérique, les équations de Navier-Stokes sont résolues,en formulation faiblement compressible, au moyen du solveur CHOC-WAVES, basé sur le schéma WENO. L’approche DNS est justifiée par l’absence, dans la littérature, de modèles de sous-maille capables de prendre en compte les effets de la viscosité variable. Les équations de transport des différentes grandeurs moyennes et fluctuantes en un point et en chaque échelle (bilan d’énergie cinétique) sont réécrites en formulations incompressible et à viscosité variable. Des termes supplémentaires, engendrés par les variations spatio-temporelles de la viscosité, apparaissent dans ces équations. Celles-ci sont utilisées comme outil, afin d’explorer l’écoulement de couche de mélange et d’étudier le développement de la turbulence dans un milieu hétérogène. Les rapports de viscosité simulés sont Rv = [1−18]. Les résultats numériques montrent que l’épaisseur de la zone de mélange δθ évolue plus rapidement lorsque le rapport de viscosité Rv est élevé. De même, les gradients verticaux de la vitesse longitudinale sont amplifiés par les gradients de viscosité, un gain de près de 60%, par rapport aux valeurs initiales, est observé. La production de l’énergie cinétique turbulente est également amplifiée.L’évolution temporelle des fluctuations des vitesse est accélérée, celles-ci sont augmentées de près de 120% par rapport à l’écoulement à viscosité constante. Le régime autosimilaire du tenseur de Reynolds est atteint plus rapidement par l’écoulement à viscosité variable et l’isotropie des fluctuations de vitesse est améliorée. / Since the pioneering work of Brown and Roshko on the effects of density variations within the mixed layer flow, several other theoretical, experimental and numerical studies harnessed to finely investigate this flow. The motivations are of practical order (chemical industry, aerodynamics, combustion. . .) or purely theoretical (the role of coherent structures,secondary instabilities). These studies have focused on, among others, the effects of compressibility and/or variable density. To our knowledge, the effects of viscosity variations in the mixing layer configuration are not discussed in the literature. The objective of this researchis the theoretical and numerical exploration of the variable viscosity temporal mixedlayer flow, especially during its initial phase of development. From a numerical viewpoint, the Navier-Stokes equations are solved in weakly compressible formulation, using the solver CHOC-WAVES, based on WENO scheme. The DNS approach is justified by the absence in the literature of subgrid models that account for the effects of variable viscosity. The transport equations of different mean and fluctuating quantities at a point and each scale (scale-by-scale energy budget) are rewritten in incompressible and variable-viscosity formulation. Additional terms, generated by the spatial and temporal variations of viscosity occur in these equations. These are used as a tool to explore the mixed layer flow and study the development of turbulence in a heterogeneous environment. The simulated viscosity ratios are Rv = [1 − 18]. The numerical results show that the mixing layer thickness δθ growsfaster when the viscosity ratio Rv is high. The vertical gradients of the longitudinal mean velocity are amplified by the viscosity gradients, a gain of almost 60 %, compared to initial values was observed. The production of turbulent kinetic energy is also amplified. The temporal evolution of the velocity fluctuations is accelerated, they are increased to nearly 120 % with respect to the constant viscosity flow. The self-similar regime of the Reynolds tensor is reached more quickly by the variable viscosity flow and the isotropy of the velocity fluctuations is improved.

L’objectif de cette thèse est d’étudier les caractéristiques physiques et biogéochimiques de l’habitat épipélagique (0-200 m), ses variabilités spatio-temporelles et les processus qui les gouvernent dans le Golfe de Tadjourah (Djibouti). L’analyse spectrale singulière (SSA) et la fonction empirique orthogonale (EOF) sont appliquées à deux jeux des données satellitales dérivées du radiomètre AVHRR_MetopA et des capteurs de la couleur de l’océan (Modis et Meris). Cette analyse statistique montre que les variabilités de la température de la surface de la mer (SST) et de la concentration de la chlorophylle a (CHLa) sont essentiellement expliquées par les cycles annuels et semi-annuels. Le cycle annuel de la SST montre l’alternance des eaux chaudes d’avril à octobre et des eaux froides de novembre à mars. Le cycle semi-annuel indique une légère baisse de la SST entre juillet et aout, particulièrement à l’ouest du golfe. Pour la CHLa, la variabilité est entièrement représentée par le cycle annuel. Celui-ci indique l’enrichissement des eaux du large avec un fort gradient côte-large de juillet à novembre et une tendance inverse de décembre à juin. En outre, l’analyse spectrale singulière multi-canal (M-SSA) et la fonction de corrélation croisée avec fenêtre de 120 jours, appliquées à l’ensemble des paramètres océanique (SST et CHLa) et atmosphériques (Vent, Température et humidité spécifique de l’air) révèlent que le cycle annuel de la SST est relié aux flux de chaleur à l’interface air-mer. En revanche, le refroidissement des eaux durant juillet-aout associé au pic de la CHLa, a été attribué au phénomène d’upwelling. Dans la seconde partie, afin d’élucider l’influence océanique sur la SST et la CHLa, les structures thermohalines and biogéochemiques de la couche supérieure (0-200 m) sont étudiées à l’aide des données collectées durant juillet-aout 2013, septembre 2013 et Février 2014. Les résultats montrent qu’en juillet-aout, la couche superficielle se composait d’une couche de mélange (CM) s’étendant sur environ 20-30 m de profondeur, suivie d’une thermocline localisée entre 30 and 50 m. La CM était réduite à l’ouest et au sud-est du golfe où le gradient thermique et la CHLa étaient plus élevées proche de la surface. En septembre, cette stratification persistait mais la CM était plus chaude et salée. En Février, la CM s’étendait sur environ 120 m de profondeur et la thermocline était moins prononcée. La comparaison des courants mesurés avec les courants de dérive d’ekman et les courants géostrophiques ont révélé que les structures thermohalines et biogéochimiques sont influencées par les vents de moussons du Sud-Ouest (MSO) et du Nord-Est (MNE). Les MSO qui soufflent de juin à aout, déplacent les eaux de surface du Golfe de Tadjourah vers le Golfe d’Aden et induisent la remontée des eaux profondes à l’ouest et l’intrusion par le nord-est des eaux salée de la thermocline. Celle-ci se rapproche de la surface particulièrement à l’ouest où elle se mélange avec les eaux de surface. En revanche, les vents de moussons du nord-est (MNE) prédominants de novembre à mai, emmènent les eaux froides vers le Golfe de Tadjourah. Le mélange convectif profond épaissit la CM. Cette thèse montre que les vents de moussons et leur renverse saisonnière jouent un rôle crucial dans la stratification de la colonne d’eau et que la topographie du bassin influence et module leurs effets. Durant l’été, la forme en cuvette du bassin et la pente continentale plus allongée à l’ouest favorise l’upwelling à l’ouest du golfe où les anomalies de la SST et de fortes concentrations de la CHLa ont été observées. / The objective of this thesis is to study the physical and biogeochemical characteristics of the pelagic habitat (0-200m), its spatio-temporal variability and the processes that govern them in the Gulf of Tadjourah (Djibouti).Singular spectrum analysis (SSA) and empirical orthogonal function (EOF) were applied to two data sets derived from AVHRR_MetopA radiometry and sea colour sensors (Modis and Meris). These statistical analysis shows that the variability of sea surface temperature (SST) and chlorophyll a concentration (CHLa) are mainly explained by annual and semi-annual cycles. The annual cycle of SST consists of an alternation between warmer (April to October) and cooler (November to March) surface water. The semi-annual cycle shows a slight drop of SST between July and August, particularly in the west of the gulf. For the CHLa, the variability is fully dominated by the annual cycle indicating summer enrichment of seashore water (July-November) with a strong seaward gradient which is reversed from October to May. Multichannel spectrum analysis (M-SSA) and cross correlation function analysis applied to the oceanic (SST, CHL-a) and atmospheric parameters (wind speed, air temperature and humidity) showed that the annual cycle of SST is connected to heat flux at the air-sea interface, while the summer drop of SST and its associated CHL-a increase were attributed to upwelling. In the second part, in order to elucidate this oceanic influence on SST and CHL-a, the vertical thermohaline and biogeochemical structures of the upper layer (0-200 m) were studied using high-resolution hydrographic data collected in July-August 2013, September 2013 and February 2014. During summer, the superficial layer consisted of the mixed layer (ML) extending to a depth of about 20-30 m, followed by the thermocline located between 30 and 50 m depth. The ML was thicker in the west and the southeast where the thermal gradient and chlorophyll a concentrations were particularly high. During September, this stratification persisted but the ML became warmer and saltier and the thermocline moved slightly deeper. In February, the ML extended to about 120 m, and the thermocline was less pronounced. A comparison of the directly measured currents to the wind induced Ekman currents and to geostrophic current profiles revealed that the thermohaline and the biogeochemical features were related to the southeast and northeast monsoon winds (SWM & NEM). Between June and August, the SWM drives surface water from the Gulf of Tadjourah to the Gulf of Aden and thus induces the westward intrusion of high salinity thermocline water from the Gulf of Aden. This near surface flow mixes surface waters in the extreme west of the Gulf of Tadjourah. In contrast, the NEM which blow from September to May, bring cold water toward the Gulf of Tadjourah and thickens the ML through convective mixing. Our thesis shows that the monsoon winds and their seasonal reversal play a crucial role in the stratification of the water column, but that their effects are additionally influenced by basin topography. During summer the bowl-shape of the basin and its elongated slope in the west enhance the upwelling in this area where negative sea surface temperature anomalies and high chlorophyll a concentrations were observed.

Les cavités latérales sont des zones mortes à surface libre situées sur le côté d’un écoulement fluvial ou côtier. Les vitesses caractéristiques au sein de la cavité étant beaucoup plus faibles que celles de l’écoulement, une couche de mélange se développe à l’interface entre ces deux régions. Cette couche de mélange peut alors transférer de la quantité de mouvement de l’écoulement vers la cavité et ainsi mettre en mouvement la cavité et peut aussi transférer de la masse entre les deux régions, telle une pollution venant de l’écoulement amont. L’étude de cette thèse a alors consisté à étudier les caractéristiques de la couche de mélange, qui est rendue spécifique par le fait qu’elle se développe entre deux coins géométriques formés par l’intersection entre les parois de la cavité et celles de l’écoulement principal. Nous avons alors pu identifier l’origine et l’alternance des mouvements de fluide dans la direction transverse: de la cavité vers l’écoulement et inversement. Concernant la mise en mouvement de la cavité, le choix a été fait de considérer un écoulement principal fixé et de modifier l’extension de la cavité dans la direction perpendiculaire à l’écoulement, passant ainsi d’une cavité rectangulaire alignée avec l’écoulement principal à une cavité allongée dans le sens opposé. La mesure de champ de vitesse par PIV 2D a alors montré une forte évolution de la forme de l’écoulement à mesure que la géométrie de la cavité évolue : un système avec deux cellules alignées dans le sens de l’écoulement à un système à une seule cellule, puis un système à deux cellules et enfin un système complexe 3D ont ainsi été observés pour une cavité de plus en plus allongée. Ensuite, une modification du dispositif expérimental a permis de mesurer de deux façons différentes le transport de scalaire de l’écoulement principal vers la cavité, de comprendre les processus associés à ce transfert et enfin de quantifier cette capacité de transfert pour différents écoulements principaux et différentes géométries de cavités. Nous avons notamment montré que la géométrie de la cavité a peu d’effet alors que le nombre de Reynolds et la profondeur d’eau normalisée ont un effet majeur sur cette capacité de transfert de masse entre les deux régions. / Lateral cavities are free-surface dead-zones located on the side of a fluvial or coastal main flow. As the typical velocities are much larger in the main flow than in the cavity, a mixing layer appears at the interface between both regions. This mixing layer is able to transfer between the main flow and the cavity momentum which then sets the fluid in the cavity in motion and also passive scalar, such as a pollution coming from upstream. The objective of this work was then to investigate the characteristics of the mixing layer, which specificity comes from the fact that it is constrained between the upstream and downstream geometrical corners. It was possible to observe the origin and alternation of the transversal fluid motions: from the cavity towards the main flow and conversely. Regarding the motion in the cavity, the choice was made to keep a constant main flow and to measure the 2D horizontal velocity field using PIV as the extension of the cavity increases. The flow pattern then passes from a 2-cell patterns aligned in the direction of the main flow to a single-cell pattern, then a 2-cells patterns aligned along the direction perpendicular to the main flow and finally a complex 3D pattern for the widest cavity. Then a modification of the experimental set-up permitted to investigate the passive scalar exchanges from the main stream towards the cavity. It was possible to understand the processes responsible for such transfer and to quantify the transfer capacity. The analysis dimensional revealed that in the present subcritical, smooth simplified geometry cavity, the three parameters possible responsible for the modification of the transfer capacity are the geometrical aspect ratio of the cavity, the Reynolds number of the main flow and finally the normalized water depth. It was then shown that the impact of the cavity geometry remains negligible but that the Reynolds number and the normalized water do impact this passive scalar transfer capacity.

Cette étude porte sur le calcul numérique du champ acoustique rayonné par des écoulements subsoniques turbulents présentant des inhomogénéités de température. Des méthodes hybrides sont développées grâce à un développement de Janzen-Rayleigh des équations de Navier-Stokes. L'écoulement est résolu par un calcul quasi incompressible puis les perturbations acoustiques sont propagées selon deux méthodes : les équations d'Euler linéarisées (EEL) et l'approximation à faible nombre de Mach perturbée(PLMNA). Les méthodes sont validées sur des cas simples puis appliquées à une couche de mélange isotherme et anisotherme en développement spatial. / This study focuses on the numerical calculation of the acoustic field radiated by subsonic turbulent flows with temperature inhomogeneities. Hybrid methods are developed through a Rayleigh-Janzen expansion of the Navier-Stokes equations. The flow is solved in a quasi-incompressible way then the acoustic disturbances are propagated by two methods : the linearized Euler's equations (EEL) and the perturbed low Mach number approximation (PLMNA). The methods are validated on simple cases and then applied to an isothermal and non isothermal spatially evolving mixing layer.

This thesis is concerned with the study of parallel mixing of two dissimilar gases under compressible conditions in the confined environment. A number of numerical studies are reported in the literature for the compressible mixing of two streams of gases where (1) both the streams are of similar gases at the same temperatures, (2) both the streams are at different temperatures with similar gases, and (3) dissimilar gases are with nearly equal temperatures. The combination of dissimilar gases at large temperature difference, mixing under compressible conditions, as in the case of scramjet propulsion, has not been adequately addressed numerically. Also many of the earlier studies have used two dimensional numerical simulation and showed good match with the experimental results on mixing layers that are inherently three dimensional in nature. In the present study, both two-dimensional (2-d) and three dimensional (3-d) studies are reported and in particular the effect of side wall on the three dimensionality of the flow field is analyzed, and the reasons of the good match of two dimensional simulations with experimental results have been discussed. Both two dimensional and three dimensional model free simulations have been conducted for a flow configuration on which experimental results are available. In this flow configuration, the mixing duct has a rectangular cross section with height to width ratio of 0.5. In the upper part of the duct hydrogen gas at a temperature of 103 K is injected through a single manifold of two Ludweig tubes and in the lower part of the duct nitrogen gas at a temperature of 2436 K is supplied through an expansion tube, both the gases are at Mach numbers of 3.1 and 4.0 respectively. Measurements in the experiment are limited to wall pressures and heat flux. The choice of this experimental condition gives an opportunity to study the effect of large temperature difference on the mixing of two dissimilar gases with large molecular weights under compressible conditions. Both two dimensional and three dimensional model free simulations are carried out using higher order numerical scheme (4th order spatial and 2nd order temporal) to understand the structure and evolution of supersonic confined mixing layer of similar and dissimilar gases. Two dimensional simulations are carried out by both SPARK (finite difference method) and OpenFOAM (finite volume method based open source software that was specially picked out and put together), while 3D model free simulations are carried out by OpenFOAM. A fine grid structure with higher grid resolution near the walls and shear layer is chosen. The effect of forcing of fluctuations on the inlet velocity shows no appreciable change in the fully developed turbulent region of the flow. The flow variables are averaged after the attainment of statistical steady state established through monitoring the concentration of inert species introduced in the initial guess. The effect of side wall on the flow structure on the mixing layer is studied by comparing the simulation results with and without side wall. Two dimensional simulations show a good match for the growth rate of shear layer and experimental wall pressures. Three dimensional simulations without side wall shows 14% higher growth rate of shear layer than that of two dimensional simulations. The wall pressures predicted by these three dimensional simulations are also lower than that predicted using two dimensional simulations (6%) and experimental (9%) results in the downstream direction of the mixing duct. Three dimensionality of the flow is thought of as a cause for these differences. Simulations with the presence of side wall show that there is no remarkable difference of three dimensionality of the flow in terms of the variables and turbulence statistics compared to the case without side walls. However, the growth rate of shear layer and wall surface pressures matches well with that predicted using two dimensional simulations. It has been argued that this good match in shear layer growth rate occurs due to formation of oblique disturbances in presence of side walls that are considered responsible for the decrease in growth rate in 3-d mixing layers. The wall pressure match is argued to be good because of hindrance from side wall in the distribution of momentum in third direction results in higher wall pressure. The effect of dissimilar gases at large temperature difference on the growth rate reduction in compressible conditions is studied. Taking experimental conditions as baseline case, simulations are carried out for a range of convective Mach numbers. Simulations are also carried out for the same range of convective Mach numbers considering the mixing of similar gases at the same temperature. The normalized growth rates with incompressible counterpart for both the cases show that the dissimilar gas combination with large temperature difference shows higher growth rate. This result confirms earlier stability analysis that predicts increased growth rate for such cases. The growth rate reduction of a compressible mixing layer is argued to occur due to reduced pressure strain term in the Reynolds stress equation. This reduction also requires the pressure and density fluctuation correlation to be very near to unity. This holds good for a mixing layer formed between two similar gases at same temperature. For dissimilar gases at different temperatures this assumption does not hold well, and pressure-density correlation coefficient shows departure from unity. Further analysis of temperature density correlation factor, and temperature fluctuations shows that the changes in density occur predominantly due to temperature effects, than due to pressure effects. The mechanism of density variations is found to be different for similar and dissimilar gases, while for similar gases the density variations are due to pressure variations. For dissimilar gases density variation is also affected by temperature variations in addition to pressure variations. It has been observed that the traditional k-ε turbulence model within the RANS (Reynolds Averaged Navier Stokes) framework fails to capture the growth rate reduction for compressible shear layers. The performance of k-ε turbulence model is tested for the mixing of dissimilar gases at large temperature difference. For the experimental test case the shear layer growth rate and wall pressures show good match with other model free simulations. Simulations are further carried out for a range of convective Mach numbers keeping the mixing gases and their temperatures same. It has been observed that a drop in the growth rate is well predicted by RANS simulations. Further, the compressibility option has been removed and it has been observed that for the density and temperature difference, even for incompressible case, the drop in growth rate exists. This behaviour shows that the decrease in growth rate is mainly due to the interaction of temperature and species mass fraction on density. Also it can be inferred that RANS with k-ε turbulence model is able to capture the compressible shear layer growth rate for dissimilar gases at high temperature difference. The mixing of heat and species is governed by the values of turbulent Prandtl and Schmidt numbers respectively. These numbers have been observed to vary for different flow conditions, while affecting the flow field considerable in the form of temperature and species distribution. Model free simulations are carried out on an incompressible convective Mach number mixing layer, and the results are compared with that of a compressible mixing layer to study the effect of compressibility on the values of turbulent Prandtl / Schmidt numbers. It has been observed that both turbulent Prandtl and Schmidt numbers show an almost constant value in the mixing layer region for incompressible case. While, for a compressible case, both turbulent Prandtl and Schmidt numbers show a continuous variation within the mixing layer. However, the turbulent Lewis number is observed to be near unity for both incompressible and compressible cases. The thesis is composed of 8 chapters. An introduction of the subject with critical and relevant literature survey is presented in chapter 1. Chapter 2 describes the mathematical formulation and assumptions along with solution methodology needed for the simulations. Chapter 3 deals with the two and three dimensional model free simulations of the non reacting mixing layer. The effect of the presence of side wall is studied in chapter 4. Chapter 5 deals with the effect of compressibility on the mixing of two dissimilar gases at largely different temperatures. The performance of k-ε turbulence model is checked for dissimilar gases in Chapter 6. Chapter 7 is concerned with the effect of compressibility on turbulent Prandtl and Schmidt numbers. Finally concluding remarks are presented in chapter 8. The main aim of this thesis is the exploration of parallel mixing of dissimilar gases under compressible conditions for both two and three dimensional cases. The outcome of the thesis is (a) a finding that the presence of sidewall in a mixing duct does not make flow field two dimensional, instead it causes the formation of oblique disturbances and the shear layer growth rate is reduced, (b) that it has been shown that the growth rates of dissimilar gases are affected far more by large temperature difference than by compressibility as in case of similar gases, (c) that the growth rates of compressible shear layers formed between dissimilar gases are better predicted using k-εturbulence model and (d) that for compressible mixing conditions the turbulent Prandtl and Schmidt numbers vary continuously in the mixing layer region necessitating the use of some kind of model instead of assuming constant values.

L’approximation dite « anélastique » permet de filtrer les ondes acoustiques grâce à un développement asymptotique deséquations de Navier-Stokes, réduisant ainsi le pas en temps moyen, lors de la simulation numérique du développement d’instabilités hydrodynamiques. Ainsi, les équations anélastiques sont établies pour un mélange de deux fluides pour l’instabilité de Rayleigh-Taylor. La stabilité linéaire de l’écoulement est étudiée pour la première fois pour des fluides parfaits, par la méthode des modes normaux, dans le cadre de l’approximation anélastique. Le problème de Stokes issu des équations de Navier-Stokes sans les termes non linéaires (une partie de la poussée d’Archiméde est prise en compte) est défini ; l’éllipticité est démontrée, l’étude des modes propres et l’invariance liée à la pression sont détaillés. La méthode d’Uzawa est étendue à l’anélastique en mettant en évidence le découplage des vitesses en 3D, le cas particulier k = 0 et les modes parasites de pression. Le passage au multidomaine a permis d’établir les conditions de raccord (raccord Co de la pression sans condition aux limites physiques). Les algorithmes et l’implantation dans le code AMENOPHIS sont validés par les comparaisons de l’opérateur d’Uzawa développé en Fortran et à l’aide de Mathematica. De plus des résultats numériques ont été comparés à une expérience avec des fluides incompressibles. Finalement, une étude des solutions numériques obtenues avec les options anélastique et compressible a été menée. L’étude de l’influence de la stratification initiale des deux fluides sur le développement de l’instabilité de Rayleigh-Taylor est amorcée. / The « anelastic » approximation allows us to filter the acoustic waves thanks to an asymptotic development of the Navier-Stokes equations, so increasing the averaged time step, during the numerical simulation of hydrodynamic instabilitiesdevelopment. So, the anelastic equations for a two fluid mixture in case of Rayleigh-Taylor instability are established.The linear stability of Rayleigh-Taylor flow is studied, for the first time, for perfect fluids in the anelastic approximation.We define the Stokes problem resulting from Navier-Stokes equations without the non linear terms (a part of the buoyancyis considered) ; the ellipticity is demonstrated, the eigenmodes and the invariance related to the pressure are detailed.The Uzawa’s method is extended to the anelastic approximation and shows the decoupling speeds in 3D, the particular casek = 0 and the spurius modes of pressure. Passing to multidomain allowed to establish the transmission conditions.The algorithms and the implementation in the existing program are validated by comparing the Uzawa’s operator inFortran and Mathematica langages, to an experiment with incompressible fluids and results from anelastic and compressiblenumerical simulations. The study of the influence of the initial stratification of both fluids on the development of the Rayleigh-Taylor instability is initiated.