  J.-Y. Chemin proved the convergence (as the Rossby number $\epsilon$ goes to
zero) of the solutions of the Primitive Equations to the solution of the 3D
quasi-geostrophic system when the Froude number F = 1 that is when no
dispersive property is available. The result was proved in the particular case
where the kinematic viscosity $\nu$ and the thermal diffusivity $\nu$ ' are
close. In this article we generalize this result for any choice of the
viscosities, the key idea is to rely on a special feature of the
quasi-geostrophic structure.
