  A finite element method for the numerical solution of the anisotropic
Navier-Stokes equations in shallow domain is presented. This method take into
account aspect ratio in the hydrostatic approximation of the Navier-Stokes
equations \cite{beslay,azthese,azgui}. A projection method \cite{guermond,shen}
is used for the time discretization. The linear systems are solved via a some
preconditioned conjugate algorithm, well adapted to massively parallel
computers \cite{julien_these,julien_precond,julien_precond_paral}. Some results
are presented for the wind driven water circulation in the North Atlantic.
