The most important component of the climate system over the Indian Ocean region is the southwest monsoon, which dictates the life and economy of billions of people in the tropics. Being a phenomena that involves interaction between atmosphere, ocean and land, the southwest monsoon is strongly influenced by upper ocean, primarily through warm sea surface temperature (SST). This is particularly true about the southeastern Arabian Sea (SEAS) and the onset of southwest monsoon over the peninsular India. A localized patch of warm water, known as the Arabian Sea mini warm pool (ASMWP), forms in the SEAS during February–March. It remain as the warmest spot in the northern Indian Ocean till early April. A large region, surrounding the SEAS, attains SST exceeding 30°C during April–May, with often the ASMWP as its core. The ASMWP is believed to have a critical impact on the air-sea interaction during the onset phase of southwest monsoon and on the formation of the onset vortex, during late May or early June. This thesis addresses the formation mechanisms of ASMWP, using a high-resolution Ocean General Circulation Model (OGCM) of the Indian Ocean. In addition to the formation of ASMWP, the SEAS is characterized by several features in its hydrography and circulation, which have been invoked in the past to explain the preferential warming of this oceanic region. During November–January, the prevailing surface currents transport low-salinity water from the Bay of Bengal into the SEAS and leads to strong haline stratification in the upper layer and formation of barrier layer (layer between mixed layer and isothermal layer). The vertical distribution of temperature in the SEAS exhibit inversions (higher subsurface temperature than that at surface) during December–February. A high in sea level and anticyclonic eddies develop in the SEAS during December and they propagate westward. These eddies modify the hydrography through downwelling and play an important role in the redistribution of advected low-salinity water within the SEAS. The seasonally reversing coastal and equatorial currents present in and around SEAS also have a major contribution in setting up the hydrography, through the advection and redistribution of cooler low-salinity water. These features make the SEAS a unique oceanographic region. The first hypothesis on the formation of ASMWP, which has been suggested by diagnostic studies, is based on the barrier layer mechanism. The barrier layer, caused by the influx of low-salinity water at surface, is argued to maintain a shallow mixed layer which can warm more efficiently. In addition, presence of barrier layer can prevent mixed layer cooling, by cutting off the interaction of mixed layer with cooler thermocline water below. However, a coupled model study have shown that there is no significant impact on the ASMWP formation from barrier layer, but only a weak warming effect during it mature phase during April. The second hypothesis, which is based on an OGCM study, has suggested that the temperature inversions present within the barrier layer can heat the mixed layer through turbulent entrainment and in turn lead to the formation of ASMWP during February–March. Both hypotheses rule out the possibility of air-sea heat fluxes being the primary reason in its formation. The strong salinity stratification in the SEAS during December–March is central to the hypotheses about formation of the ASMWP. Observational studies have only limited success in assessing the contribution from barrier layer and temperature inversions, as the ASMWP always form in their presence. OGCMs offer a better alternative. However, modelling processes in the northern Indian Ocean, especially that in the SEAS, is a challenging problem. Previous Indian Ocean models have had serious difficulties in simulating the low-salinity water in the Bay of Bengal and its intrusion into the SEAS. The northward advection of low-salinity water in the SEAS, along the west coast of India, is used to be absent in model simulations. Moreover, the coarse resolution inhibited those models from simulating faster surface currents and vigorous eddies as seen in the observations. In this thesis, we use an OGCM of the Indian Ocean, based on the recent version of Modular Ocean Model (MOM4p0), to study the ASMWP. The model has high resolutions in the horizontal (1/4o x 1/4o) and vertical (40 levels, with 5 m spacing in upper 60 m), and has been forced with daily values momentum, heat and freshwater fluxes. The turbulent (latent and sensible) and long wave heat fluxes have been calculated as a function of model SST. The freshwater forcing consists of precipitation, evaporation and river runoff, and there are no surface restoring or flux adjustments. The river runoff has been distributed over several grid points about the river mouth instead of discharging into a singe grid point, which has resulted in remarkable improvements in salinity simulation. The model simulates the Indian Ocean temperature, salinity and circulation remarkably well. The pattern of model temperature distribution and evolution matches very well with that in the observations. Significant improvements have been made in the salinity simulation, including the Bay of Bengal freshwater plume and intrusion of low-salinity water from the bay into the SEAS. The salinity distribution within the SEAS is also well represented in the model. The use of appropriate horizontal friction parameters has resulted in the simulation of realistic currents. The observed features in the SEAS, including the life cycle of the ASMWP, low-salinity water, barrier layer, temperature inversions, eddies and currents are well represented in the model. Present study has unraveled the processes involved in the life cycle of barrier layer and temperature inversions in the SEAS. Presence of low-salinity water is necessary for their formation. Barrier layer develops in the SEAS during November, after the intrusion of low-salinity water from the Bay of Bengal. The barrier layer is thickest during January–February, and it dissipates during March–April. The variations and peak of barrier layer thickness is controlled by variations in isothermal layer depth, which in turn is dominated by the downwelling effects of anticyclonic eddies. The intense solar heating during March–April leads to the formation of shallow isothermal layer and results in the dissipation of barrier layer. Temperature inversions starts developing in the SEAS during December, reaches its peak during January–February and dissipates in the following months. Advection of cooler low-salinity water over warmer salty water and penetrating shortwave radiation is found to cause temperature inversions within the SEAS, whereas winter cooling is also important to the north and south of the SEAS. There is significant variation in the magnitude, depth of occurrence and formation mechanisms of temperature inversions within the SEAS. Analysis of model mixed layer heat budget has shown that the SEAS SST is mainly controlled by atmospheric forcing, including the life cycle of ASMWP. It has also shown that the heating from temperature inversions do not contribute to the formation of ASMWP. In an experiment in which a constant salinity of 35 psu was maintained over the entire model domain, the ASMWP evolved very similar to that in the standard run, suggesting that the salinity effects are not necessary for the formation of ASMWP. Examination of wind field show that the winds over the SEAS during November–February are low due to the blocking of northeasterly winds by Western Ghats. Several process experiments by modifying the wind and turbulent heat fluxforcing fields have shown that these low winds lead to the formation of ASMWP in the SEAS during February–March. The low winds reduce latent heat loss, resulting in net heat gain by the ocean. This helps the SEAS to keep warmer SST while the surrounding region experience intense cooling under the strong dry northeasterly winds. As the winds are weak over the SEAS, the mixed layer is not able to feel the stratification beneath and the mixed layer depth is determined by solar heating, with or without salinity effects. In addition, the weak winds are not able to entrain the temperature inversions present in the barrier layer. The winds are weak during March–April too, and the air-sea heat fluxes dictate the SST evolution during this period. Therefore, during November–April, the SEAS acts as a low wind heat-dominated regime, where the evolution of sea surface temperature is solely determined by atmospheric forcing. We show that, in such regions, the evolution of surface layer temperature is not dependent on the characteristics of subsurface ocean, including the presence of barrier layer and temperature inversions.

La mer des Salomon est une mer semi-fermée située dans le Pacifique subtropical. Elle connecte les masses d'eau des subtropiques à l'équateur via les courants de bord ouest de faibles latitudes (LLWBCs) et pourrait de ce fait moduler à l'échelle décennale le climat du Pacifique tropical. Très peu d'observations sont disponibles pour l'étude de cette région. Un des objectifs principaux de cette étude est la mise en place d'un modèle réaliste d'océan à haute résolution (1/36°) de la mer des Salomon permettant la résolution d'une large gamme d'échelles, particulièrement la mésoéchelle et marginalement la sous-mésoéchelle. La circulation générale est étudiée ainsi que la variabilité à mésoéchelle et à sous-mésoéchelle. La représentation de la circulation simulée par le modèle 1/36° est non seulement validée par les observations disponibles mais aussi améliorée par rapport à celle simulée par les modèles antérieurs. La variabilité mésoéchelle simulée dans le modèle à haute résolution est fortement augmentée par rapport à celle issue des modèles antérieurs et est en bon accord avec les observations. Des études spectrales en nombre d'onde de la température de surface, de la dénivellation de la surface libre et de l'énergie cinétique ont été réalisées dans la mer des Salomon et suggèrent que les pentes spectrales obtenues sont proches de la théorie classique de la quasi-géostrophie de surface (SQG). / The Solomon Sea is a semi-closed sea located in the subtropical Pacific Ocean. It connects subtropical water masses to the equatorial one through the low latitude western boundary currents (LLWBCs) and could potentially modulate the tropical Pacific climate at decadal time-scales. This region is not well documented because of few available observations. One of the main objective of this study is to set up a high resolution realistic ocean model of the Solomon at 1/36° that will allow to resolve a broad range of scales, especially the mesoscale and partially the sub-mesoscale processes. The general circulation and the mesoscale and sub-mesoscale variabilities are studied. The representation of the high resolution circulation is consistent with the available observations and is better resolved than in previous coarser resolution models. The mesoscale variability in the high resolution model is strongly increased compared to that of previous models and is in a good agreement with the observations. SST, SSH and kinetic energy wavenumber spectra in the Solomon Sea show spectral slopes closed to the surface quasi-geostrophy SQG theory.

Les écoulements en eau peu profonde se rencontrent dans de nombreuses situations d’intérêts : écoulements de rivières et dans les lacs, mais aussi dans les mers et océans (courants de marée, tsunami, etc.). Ils sont modélisés par un système d’équations aux dérivées partielles, où les inconnues sont la vitesse de l’écoulement et la hauteur d’eau. On peut supposer que la composante verticale de la vitesse est petite devant les composantes horizontales et que ces dernières sont indépendantes de la profondeur. Le modèle est alors donné par les équations de shallow water (SWEs). Cette thèse se concentre sur la conception d’une nouvelle technique d’interaction de plusieurs grilles imbriquées pour modèle en eau peu profonde en utilisant des méthodes numériques. La première partie de cette thèse comprend, La dérivation complète de ces équations à partir des équations de Navier- Stokes est expliquée. Etudier le développement et l’évaluation des méthodes numériques en utilisant des méthodes de différences finies et plusieurs exemples numériques sont appliqués utilisant la condition initiale du niveau gaussien pour 2DSWEs. Dans la deuxième partie de la thèse, nous sommes intéressés à proposer une nouvelle technique d’interaction de plusieurs grilles imbriquées pour résoudre les modèles océaniques en utilisant quatre choix des opérateurs de restriction avec des résultats de haute précision. Notre travail s’est concentré sur la résolution numérique de SWE par grilles imbriquées. A chaque niveau de résolution, nous avons utilisé une méthode classique de différences finies sur une grille C d’Arakawa, avec un schéma de leapfrog complété par un filtre d’Asselin. Afin de pouvoir affiner les calculs dans les régions perturbées et de les alléger dans les zones calmes, nous avons considéré plusieurs niveaux de résolution en utilisant des grilles imbriquées. Ceci permet d’augmenter considérablement le rapport performance de la méthode, à condition de régler efficacement les interactions (spatiales et temporelles) entre les grilles. Dans la troisième partie de cette thèse, plusieurs exemples numéériques sont testés pour 2DSWE avec imbriqués 3:1 et 5:1. Finalement, la quatrième partie de ce travail, certaines applications de grilles imbriquées pour le modèle tsunami sont présentées. / Most flows in the rivers, seas, and ocean are shallow water flow in which the horizontal length andvelocity scales are much larger than the vertical ones. The mathematical formulation of these flows, so called shallow water equations (SWEs). These equations are a system of hyperbolic partial differentialequations and they are effective for many physical phenomena in the oceans, coastal regions, riversand canals. This thesis focuses on the design of a new two-way interaction technique for multiple nested grids 2DSWEs using the numerical methods. The first part of this thesis includes, proposing several ways to develop the derivation of shallow water model. The complete derivation of this system from Navier-Stokes equations is explained. Studying the development and evaluation of numerical methods by suggesting new spatial and temporal discretization techniques in a standard C-grid using an explicit finite difference method in space and leapfrog with Robert-Asselin filter in time which are effective for modeling in oceanic and atmospheric flows. Several numerical examples for this model using Gaussian level initial condition are implemented in order to validate the efficiency of the proposed method. In the second part of our work, we are interested to propose a new two-way interaction technique for multiple nested grids to solve ocean models using four choices of higher restriction operators (update schemes) for the free surface elevation and velocities with high accuracy results. Our work focused on the numerical resolution of SWEs by nested grids. At each level of resolution, we used explicit finite differences methods on Arakawa C-grid. In order to be able to refine the calculations in troubled regions and move them into quiet areas, we have considered several levels of resolution using nested grids. This makes it possible to considerably increase the performance ratio of the method, provided that the interactions (spatial and temporal) between the grids are effectively controlled. In the third part of this thesis, several numerical examples are tested to show and verify twoway interaction technique for multiple nested grids of shallow water models can works efficiently over different periods of time with nesting 3:1 and 5:1 at multiple levels. Some examples for multiple nested grids of the tsunami model with nesting 5:1 using moving boundary conditions are tested in the fourth part of this work.