Schémas numériques d'advection et de propagation d'ondes de gravité pour les modèles de circulation océanique

Keywords :

• modélisation numérique
• ondes de gravité
• splitting barotrope/barocline
• schémas d'advection
• diffusion diapycnale
• schémas multidimensionnels
• oceanic circulation
• numerical modeling
• gravity waves
• barotropic/baroclinic splitting
• advection schemes
• diapycnal diffusion
• multidimensional schemes

Three-dimensional regional ocean numerical models are based on the primitive equations solution. Most of them use finite differences methods on staggered grids. These models have to accurately represent transports and energy transfers. Improving these numerical models therefore requires (i) the identification of predominant processes, particularly in terms of dissipation and (ii) the derivation of numerical methods satisfying a number of equilibrium.
The first part of the work focuses on the propagation of external and internal gravity waves.
We first focus on the stability of the separation in fast (barotropic) mode and slow (baroclinic) modes and show that it can be improved by removing some usual. In a second step, we study the impact of the discretization (schemes orders, grid staggering) on the propagation of internal gravity waves coming from the velocity pressure coupling. A decomposition into vertical modes also allows us to introduce a highly effective space-time scheme. The second part deals with the numerical advection schemes of momentum and tracers, especially with the aim of reducing the diapycnal diffusion (diffusion in the direction orthogonal to constant density layers). This work leads us first to focus our attention on the vertical advection schemes often neglected compare with the horizontal dimension. The good properties of a compact scheme (and its space-time and monotone variants ) are highlighted. Finally we analyze the multidimensional behavior of these advection schemes.

Directors:

• Mr Laurent Debreu (Chargé de Recherche - INRIA )
• Mr Patrick Marchesiello (Directeur de Recherche - IRD-LEGOS )
• Mr Eric Blayo-Nogret (Professeur - Université Joseph Fourier )

Raporteurs:

• Mr Daniel Le Roux (Professeur - Université Claude Bernard Lyon 1 )
• Mr Gurvan Madec (Directeur de Recherche - CNRS-LOCEAN )

Examinators:

• Mr Emmanuel Maitre (Professeur - Grenoble INP )
• Mr Emmanuel Audusse (Maître de Conférences - Université Paris 13 )
• Mme Virginie Daru (Maître de Conférence - ENSAM Paris-tech/CNRS-LIMSI )