In this paper, we study the quasi-geostrophic approximation of the Navier-Stokes equations. This approximation is usually used in modelisation of oceanic circulations. First, we consider the barotropic modelisation, and in a second part, we supposed that the ocean is divided in N layers. For the both modelisations, we prove the existence and uniqueness of the solution, and then the existence of a maximal attractor which describes the long time behaviour of the solutions and we derive estimates of its Hausdorff and fractal dimensions in terms of the data.
