Abstract : This work is dedicated to the numerical computations of the primitive equations (PEs) of the ocean without viscosity with nonlocal (mode by mode) boundary conditions. We consider the 2D nonlinear PEs, and firstly compute the solutions in a "large" rectangular domain D with periodic boundary conditions in the horizontal direction. Then we consider a subdomain D', in which we compute a second numerical solution with transparent boundary conditions. Two objectives are achieved. On the one hand the absence of blow-up in these computations indicates that the PEs without viscosity are well-posed when supplemented with the boundary conditions. On the other hand they show a very good coincidence on the subdomain D' of the two solutions, thus showing also the computational relevance of these new boundary conditions. We end this study with some numerical simulations of the linearized primitive equations, which correspond to the theoretical results established by the authors, and evidence the transparent properties of the boundary conditions.
