In this paper we propose a strategy to approximate incompressible hydrostatic
free surface Euler and Navier-Stokes models. The main advantage of the proposed
models is that the water depth is a dynamical variable of the system and hence
the model is formulated over a fixed domain.The proposed strategy extends
previous works approximating the Euler and Navier-Stokes systems using a
multilayer description. Here, the needed closure relations are obtained using
an energy-based optimality criterion instead of an asymptotic expansion.
Moreover, the layer-averaged description is successfully applied to the
Navier-Stokes system with a general form of the Cauchy stress tensor
