# Séminaire

**Titre :**The three dimensionalization of barotropic instability

**Nom du conférencier :**Francis POULIN

**Son affiliation :**Department of Applied Mathematics, University of Waterloo, Canada

**Laboratoire organisateur :**LMD

**Date et heure :**10-06-2010 11h00

**Lieu :**LMD-ENS, 24 rue Lhomond, salle E314 (ex-316) du Dept des Géosciences

**Résumé :**

The ocean contains a variety of motions over a vast range of length and time scales. The general circulation of the ocean is predominantly forced at the surface on synoptic length-scales, whereas the dissipation due to molecular viscosity is on length scales less than a centimeter. The mechanisms through which the ocean cascades energy have been intensely studied and at present the component of the oceanic energy budget that is least understood is the transfer of energy from the mesoscale to the submesoscale. The generation of a submesoscale energy cascade can arise due to unbalanced motions, one important example of which is the instability of shear flows. Molemaker, McWilliams and Yavneh (2005) have studied the downscale cascade induced by baroclinic instability in a primitive equation model. It is found that by accurately resolving the small scale processes, the downscale cascade can be enhanced. In this work we begin a similar study but in the context of barotropic instability. Poulin and Flierl (2003) studied the instability of a barotropic Bickley jet in the context of the Shallow Water Model. They found that with order one Rossby numbers and large free-surface displacements, there can be a strong asymmetry between cyclones and anticyclones. Perret et al. (2006) found asymmetries in the frontal regime with order one Rossby numbers. The aim of this study are as follows: 1) Investigate the barotropic instability with order one Rossby and Burger numbers with relatively weak stratification. 2) Determine the effect of increasing vertical resolution has on resolving the 3D instability, both in the early onset and after the nonlinear adjustment. 3) We compare the effect of the Non-Traditional (NT) Coriolis parameters versus making the Traditional Approximation (TA). This is because the NT terms can transfer momentum between the zonal and vertical directions thereby inducing vertical velocities.

**Contact :**

Riwal Plougonven, 01 44 32 27 31