This thesis addresses modeling transport phenomena in porous media with special attention being paid to convective characteristics of variable viscosity fluids in a homogeneous and isotropic medium. Two different categories of flows, with totally different driving forces, are considered being forced and free convection (both side and bottom heating, for a square enclosure, are studied). To account for property variation, the density is modeled by an Oberbeck–Boussinesq approximation while the viscosity is modeled by an exponential function. The limitations of the previous work, addressing the issue, are discussed in detail and improvements, in terms of thermo-hydraulic performance of the system are suggested. Dealing with the global aspects of the problem, the two major methods being the reference temperature and the property ratio approach are implemented. For natural convection problems, the former method is used; while for forced convection the latter is undertaken. New correlations, which are proved to be more accurate, are proposed for both forced and free convection problems. Besides, closed form solutions are reported for some cases of constant and variable viscosity. Convection visualization is also studied in detail where the concept of Energy Flux Vectors is put forward along with the application of heatlines and energy streamlines. It was mathematically shown that in two-dimensional space heatlines and energy streamlines, which were invented independently, are the same as each other. Moreover, the newly developed concept, energy flux vectors serve as a new tool for convection visualization with the main advantage that this new technique, unlike heatlines and energy streamlines, does not require further (and sometimes complicated) numerical analysis in addition to solving momentum and thermal energy equations. This, in its turn, reduces the time and computer resources required to see the flow of energy. Finally, in Chapter 7, the summary of the work along with the conclusions are presented. Finally, recommendations for future studies are put forward.

Numerical study of laminar convective cooling of ribs in a parallel plate channel is investigated. Single rib mounted on one channel wall in forced, mixed and free convection is analyzed. Furthermore, the series ribs array with in-line and staggered mounted on channel walls are considered. Through the use of a stream function vorticity transformation, solution of the transformed governing equations for the system is obtained using the control volume method with non-uniform grid. The effects of the Reynolds number, thermal conductivity ratio of rib to fluid and rib¡¦s profile area on heat transfer rate of single rib and rib array are presented. In addition, the effects of the length from inlet to the first rib and the space between ribs for rib array are carried out. A correlation for single and rib array in forced convection is presented to estimate the optimum aspect ratio of rib with various Reynolds number, thermal conductivity ratio of rib to fluid, rib¡¦s profile area. Furthermore, the results of different Gr/Re2 and various channel inclination angle in mixed convection are also examined numerically. The results indicate that both in forced and mixed convection, the optimum aspect ratio of a rib corresponding to the rib with maximum heat transfer rate increases with increasing Re but decreases with K for a fixed rib profile area. In forced convection the optimum aspect ratio of rib array increases with rib¡¦s space but decreases with the length from inlet to the first rib of channel. Then, numerical correlations to predict the optimum aspect ratio of single rib and rib array are developed for fixed rib¡¦s area with various Re, K and rib number. In mixed convection, the optimum aspect ratios of single rib and staggered rib array increase with not only the inclination angle but also Gr/Re2.

We investigate the role of boundary layer forcing and surface heterogeneities on the intensity and spectral distribution of the convective circulations of an idealized convective system. Our ultimate goal is to further the understanding of atmospheric convection. However, we depart from realistic atmospheric convection and study an idealized convective system known as the Rayleigh-Benard model in two dimensions. We extended the classical Rayleigh-Benard model to include the effects of boundary heterogeneities. These effects are included, inparticular through a sinusoidally variable surface temperature. In this idealized model, the Rayleigh number plays the role of convective available potential energy (CAPE) in atmospheric convection, while the boundary heterogeneities in the temperatureplay the role of boundary layer forcing. In particular, we study the effects of boundary forcing on the intensity and spectral distribution of convective circulations in great detail.We consider the problem in the linear and weakly nonlinear regimes. In the linear regime, we find an analytical solution for Rayleigh-Benard convection with boundary forcing. We show that the inclusion of periodic boundary forcing causes discontinuities in the linear solution when critical conditions are approached. In the nonlinear regime, we find the solution by direct numerical simulation. The nonlinearities not only remove the discontinuities, but also lead to the appearance of non-trivial modes in the solution.The classical modes appear when the Rayleigh number issupercritical and the amplitude of the boundary forcing is small. Modes governed by boundary forcing dominate when its amplitude is large. Non-trivial modes with wavenumbers different from either the classical or the boundary modes appear only for intermediate values of the boundary forcing. The transitions between regions dominated by the classical Rayleigh forcing, mixed forcing, andboundary forcing depend on the Rayleigh number and the wavenumber of the boundary forcing. We conclude that boundary forcing has non-trivial effects on convective circulations. This result might have important implications for atmosphericconvection. Indeed, it suggests that atmospheric convection over the relatively homogeneous oceans would have different spectral distribution compared to that over heterogeneous land surfaces. This result is consistent with observations.

This thesis addresses modeling transport phenomena in porous media with special attention being paid to convective characteristics of variable viscosity fluids in a homogeneous and isotropic medium. Two different categories of flows, with totally different driving forces, are considered being forced and free convection (both side and bottom heating, for a square enclosure, are studied). To account for property variation, the density is modeled by an Oberbeck–Boussinesq approximation while the viscosity is modeled by an exponential function. The limitations of the previous work, addressing the issue, are discussed in detail and improvements, in terms of thermo-hydraulic performance of the system are suggested. Dealing with the global aspects of the problem, the two major methods being the reference temperature and the property ratio approach are implemented. For natural convection problems, the former method is used; while for forced convection the latter is undertaken. New correlations, which are proved to be more accurate, are proposed for both forced and free convection problems. Besides, closed form solutions are reported for some cases of constant and variable viscosity. Convection visualization is also studied in detail where the concept of Energy Flux Vectors is put forward along with the application of heatlines and energy streamlines. It was mathematically shown that in two-dimensional space heatlines and energy streamlines, which were invented independently, are the same as each other. Moreover, the newly developed concept, energy flux vectors serve as a new tool for convection visualization with the main advantage that this new technique, unlike heatlines and energy streamlines, does not require further (and sometimes complicated) numerical analysis in addition to solving momentum and thermal energy equations. This, in its turn, reduces the time and computer resources required to see the flow of energy. Finally, in Chapter 7, the summary of the work along with the conclusions are presented. Finally, recommendations for future studies are put forward.

This thesis addresses modeling transport phenomena in porous media with special attention being paid to convective characteristics of variable viscosity fluids in a homogeneous and isotropic medium. Two different categories of flows, with totally different driving forces, are considered being forced and free convection (both side and bottom heating, for a square enclosure, are studied). To account for property variation, the density is modeled by an Oberbeck–Boussinesq approximation while the viscosity is modeled by an exponential function. The limitations of the previous work, addressing the issue, are discussed in detail and improvements, in terms of thermo-hydraulic performance of the system are suggested. Dealing with the global aspects of the problem, the two major methods being the reference temperature and the property ratio approach are implemented. For natural convection problems, the former method is used; while for forced convection the latter is undertaken. New correlations, which are proved to be more accurate, are proposed for both forced and free convection problems. Besides, closed form solutions are reported for some cases of constant and variable viscosity. Convection visualization is also studied in detail where the concept of Energy Flux Vectors is put forward along with the application of heatlines and energy streamlines. It was mathematically shown that in two-dimensional space heatlines and energy streamlines, which were invented independently, are the same as each other. Moreover, the newly developed concept, energy flux vectors serve as a new tool for convection visualization with the main advantage that this new technique, unlike heatlines and energy streamlines, does not require further (and sometimes complicated) numerical analysis in addition to solving momentum and thermal energy equations. This, in its turn, reduces the time and computer resources required to see the flow of energy. Finally, in Chapter 7, the summary of the work along with the conclusions are presented. Finally, recommendations for future studies are put forward.

This thesis addresses modeling transport phenomena in porous media with special attention being paid to convective characteristics of variable viscosity fluids in a homogeneous and isotropic medium. Two different categories of flows, with totally different driving forces, are considered being forced and free convection (both side and bottom heating, for a square enclosure, are studied). To account for property variation, the density is modeled by an Oberbeck–Boussinesq approximation while the viscosity is modeled by an exponential function. The limitations of the previous work, addressing the issue, are discussed in detail and improvements, in terms of thermo-hydraulic performance of the system are suggested. Dealing with the global aspects of the problem, the two major methods being the reference temperature and the property ratio approach are implemented. For natural convection problems, the former method is used; while for forced convection the latter is undertaken. New correlations, which are proved to be more accurate, are proposed for both forced and free convection problems. Besides, closed form solutions are reported for some cases of constant and variable viscosity. Convection visualization is also studied in detail where the concept of Energy Flux Vectors is put forward along with the application of heatlines and energy streamlines. It was mathematically shown that in two-dimensional space heatlines and energy streamlines, which were invented independently, are the same as each other. Moreover, the newly developed concept, energy flux vectors serve as a new tool for convection visualization with the main advantage that this new technique, unlike heatlines and energy streamlines, does not require further (and sometimes complicated) numerical analysis in addition to solving momentum and thermal energy equations. This, in its turn, reduces the time and computer resources required to see the flow of energy. Finally, in Chapter 7, the summary of the work along with the conclusions are presented. Finally, recommendations for future studies are put forward.

Le but de la thèse est de comprendre l'influence dynamique des effets diabatiques, comme la convection humide, sur les instabilités des vortex atmosphériques terrestres et planétaires. Un modèle verticalement intégré, avec les paramétrisations type relaxation des transitions de phase et de dégagement de la chaleur latente, le modèle de St-Venant avec la convection humide, a été utilisé. La version précédente du modèle a été améliorée pour inclure l'eau précipitable, sa vaporisation et son entrainement. L'approche consiste en 1) analyse détaillée de stabilité des profils idéalisés, ou extraits des données, des vortex, 2) étude de saturation non-linéaire des instabilités à l'aide de schéma numérique de haute résolution aux volumes finis. Les résultats principaux de la thèse sont : 1. Démonstration et quantification d'une forte influence des effets humides sur les instabilités des vortex synoptiques, y compris asymétrie cyclone-anticyclone des vortex de faible intensité aux latitudes moyennes, et de l'intensification des vortex type cyclones tropicaux, avec formation des nuages caractéristiques. 2. Explication de l'origine dynamique de l'hexagone au pôle Nord de Saturne, et de l'absence de structure similaire au pôle Sud, en termes d'instabilité du système vortex polaire - jet circumpolaire, et sa saturation non-linéaire. 3. Explication de la structure observée du vortex polaire hivernal sur Mars en termes d'instabilité et sa saturation en présence de réchauffement /refroidissement radiatif et de déposition de CO2 (transition de phase gaz - solide). Une nouvelle paramétrisation simple a été proposée pour ce processus, incluant l'influence des noyaux de déposition. / The thesis is devoted to understanding dynamical influence of diabatic effects, like moist convection, on instabilities of vortices in Earth and planetary atmospheres. A vertically integrated atmospheric model with relaxational parameterisation of phase transitions and related heat release, and with convective fluxes included in mass and momentum equations, the moist-convective rotating shallow water model, was used for this purpose. The previous version of the model was improved to include precipitable water and its vaporisation and entrainment. The approach consists in 1)detailed stability analysis of idealised, or extracted from the data, vortex profiles, 2)study of nonlinear saturation of the instabilities with the help of finite-volume high-resolution numerical code. The main results of the thesis are: 1. Demonstration and quantification of strong influence of moist effects upon instabilities of synoptic vortices, including cyclone-anticyclone asymmetry of mid-latitude vortices of weak intensity, and intensification of tropical-cyclone like vortices with formation of typical cloud patterns. 2. Explanation of the dynamical origin of the Saturn's North Polar hexagon, and of the lack of similar structure at the South Pole, in terms of instability of the coupled polar vortex and circumpolar jet, and their nonlinear saturation.3. Explanation of the observed structure of Mars' winter polar vortex in terms of instability of the latter, and its saturation in the presence of radiative heating/cooling and CO2 deposition (gas-solid phase transition). A new simple parameterisation of the latter process, including the influence of deposition nuclei, was developed in the thesis.

Les Céphéides sont des étoiles pulsantes utilisées pour calculer les distances dans l'univers (notamment dans le Groupe Local). Elle font partie de la bande d’instabilité du diagramme de Hertzsprung-Russell. Le mécanisme κ (où κ désigne l’opacité du milieu), proposé par Eddington en 1917 pour expliquer ces variations périodiques de rayon et luminosité, est encore mal connu dans lecas de Céphéides froides (bord rouge de la bande d’instabilité) présentant une zone convective en surface.Cette thèse consiste à effectuer des simulations 3D de ces étoiles afin d’étudier l’interaction entre leurs pulsations radiales acoustiques et la convection de surface. On se ramène à un cas simple : l’étude de la propagation de modes acoustiques dans une boite cartésienne dont une partie est convective.Nous utilisons le code Heracles développé au CEA par Édouard Audit, que nous avons complété (ajout d’une étape de dissipation, passage à l’ordre 2 en temps pour l’étape de conduction).Pour valider notre code et notre modèle de Céphéide, nous reproduisons les résultats de Gastine & Dintrans (2011b) à 1D (cas purement radiatifs) et 2D (avec convection) : certaines simulations instables au κ-mécanisme (avec une saturation non-linéaire aux temps longs à 1D) redeviennent stables à 2D à cause de l’influence de la convection. La bande d’instabilité théorique du diagramme de Hertzsprung-Russell est donc trop étroite à 2D.L’hypothèse à vérifier était alors que ces Céphéides retrouvent une certaine instabilité et une saturation non-linéaire lors de simulations 3D. En effet, il est connu que les simulations 2D et 3D de convection différent à bas nombre de Prandtl, ce qui est notre cas. Dès lors, nous montrons que les panaches de convection sont en effet moins forts à 3D et ne perturbent pas autant les pulsations. On retrouve ainsi des simulations instables. Le bord rouge de la bande d’instabilité théorique est donc plus proche du bord observé à 3D qu’à 2D.Enfin, nous montrons que les modèles 1D de convection dépendante du temps de Stellingwerf (1982) et de Kuhfuss (1986) donnent des résultats similaires lorsqu’il s’agit de reproduire le profil de flux convectif des simulations 3D, lorsque la simulation présente des mouvements d’ensemble de type κ-mécanisme. Les deux modèles peinent cependant à reproduire les valeurs de ce flux convectif de manière convaincante. Cela justifie l’importance des simulations 3D. / Cepheids are pulsating stars used to calculate distances in the universe (more precisely in the Local Group). They are part of the Hertzsprung-Russell diagram’s instability strip. Their periodic variations (of luminosity and radius) are well explained by κ-mechanism, first suggested by Eddington (1917). But cold Cepheids (red edge of the instability strip) have a convective zone near their surface that affects their pulsation properties.Therefore, this PhD. thesis aims at performing 3D simulations of simplified Cepheids to study the interaction between surface convection and radial pulsations. We actually study the propagation of acoustic modes in a cartesian box partially convective.For this, we use Heracles, a hydrodynamical code developed in CEA, France, by Edouard Audit. We had to complete the code with a dissipation step and a second order (in time) conduction step (which was already available as a first order method).To validate the code and the Cepheid model used, we reproduce Gastine & Dintrans (2011b) results in 1D (radiative cases) and 2D (with convection): some setups that are unstable for κ-mecanism (with nonlinear saturation in 1D simulations) are stable in 2D thanks to convection. The theoretical Hertzsprung-Russell diagram’s instability strip is then too narrow in 2D.The hypothesis for this work was that those Cepheids would be unstable again (with saturation) in 3D due to the fact that convection grows weaker when convective plumes are 3D. 2D and 3D simulations are indeed different when Prandtl number is low as it is in our simulations. We show that pulsations are indeed not quenched anymore and that simulations are unstable. Theoretical 3D instability strip is then closer to the observed one than 2D strip was.Finally, we show that the 1D models of time-dependant convection from Stellingwerf (1982) and Kuhfuß (1986) give similar results for the convective flux of 3D convection with κ-mecanism. But none of them is able to give the exact values. That means that 3D simulations are indeed precious.

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