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The length of the mesh is $ 1$ meter, and the height is $ 0.2$ meter. The grid is composed of 12500 squared cells : $ 250 \times 50 $ (see 3.1).

Figure 3.1: Grid
\includegraphics [scale=0.8]{grid.eps}

In so far as we are in the referencial of the perturbation, boundary conditions are :

In order to better catch instabilities, the mesh is reffined in its center. Moreover, the refining of the mesh may involve numerical errors, which could be the source of perturbations. This perturbations will be amplify by the system, and we will see appear the structures.

Stephanie Terrade
Julien Delbove