In this paper we propose a stable and robust discrete model for the simulation of the 3d incompressible and hydrostatic Navier-Stokes system with free surface. The idea is use a Galerkin type approximation of the velocity field in order to obtain an accurate description of the vertical profile of the horizontal velocity. Such a strategy has several advantages. It allows : 1- to rewrite the Navier-Stokes equations under the form of a system of conservation laws with source terms, \item[$\circ$] the easy handling of the free surface, which does not require moving meshes, 2- the possibility to take advantage of robust and accurate numerical techniques developed in extensive amount for Shallow Water type systems. The proposed numerical scheme is endowed with stability properties such as positivity of the water depth, preservation of the equilibrium at rest and fully discrete entropy inequality. We confront the model and the discrete scheme with some numerical academic and realistic examples.