Multiscale approximations for ocean equations: theoretical and numerical results

Carine Lucas (1) , Christine Kazantsev (2)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
2 MOISE - Modelling, Observations, Identification for Environmental Sciences

We study a stationary Quasi-Geostrophic type equation in one or two dimensional spaces, with a quickly varying topography. We consider an asymptotic expansion of this equation on several space and time scales. At each expansion's order, we split the approximated solution into an interior function, which represents the solution far from the western boundary, and a corrector function that takes into account the boundary layer. We derive the systems at each order for the two functions and prove mathematical properties on these systems. Then we present numerical tricks and results, with and without topography, in the one and two dimensional cases. The method is very efficient compared to classical ones (finite differences, finite elements) which are very expensive due to the quickly varying topography and thin boundary layer.

Mots clés: Multiscale; existence of solutions; numerical results; boundary layer

Domaines: Equations aux dérivées partielles [math.AP]

Carine Lucas, Christine Kazantsev. Multiscale approximations for ocean equations: theoretical and numerical results. 2009. ⟨inria-00370065⟩