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

Abstract : Three-dimensional regional ocean numerical models are based on solving the primitive equations and mostly use Eulerian finite differences methods of resolution on staggered grids. These models must accurately represent transports and energy transfers. Improving these numerical models therefore requires (i) the identification of predominant process, particularly in terms of dissipation in these transfers and (ii) the construction of numerical methods respecting a number of balances. The first part of the work focuses on the propagation of external and internal gravity waves. We focus primarily on the stability of the separation in fast mode (barotropic) and slow (baroclinic) and show that it can be improved by removing certain assumptions traditionally made. In a second step, we study the impact of the discretization (order of schemes, staggered grids or not) on the propagation of internal gravity waves coming from the coupling velocity pressure. A decomposition into vertical modes also allows us to offer a highly effective space-time scheme. The second part examines in detail the numerical advection schemes of momentum and tracers, especially with the aim of reducing the diapycnal diffusion (diffusion in the orthogonal direction of constant density layers). This work leads us first to focus our attention on the vertical advection schemes often overlooked in front of the horizontal dimension. The good properties of a compact schema (and its space-time and monotonous variants ) are highlighted. Finally we analyze the multidimensional behavior of these advection schemes.
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Jérémie Demange. Schémas numériques d'advection et de propagation d'ondes de gravité dans les modèles de circulation océanique. Modélisation et simulation. Université de Grenoble, 2014. Français. ⟨NNT : 2014GRENM096⟩. ⟨tel-01104703v2⟩

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