  The standard multilayer Saint-Venant system consists in introducing fluid
layers that are advected by the interfacial velocities. As a consequence there
is no mass exchanges between these layers and each layer is described by its
height and its average velocity. Here we introduce another multilayer system
with mass exchanges between the neighborhing layers where the unknowns are a
total height of water and an average velocity per layer. We derive it from
Navier-Stokes system with an hydrostatic pressure and prove energy and
hyperbolicity properties of the model. We also give a kinetic interpretation
leading to effective numerical schemes with positivity and energy properties.
Numerical tests show the versatility of the approach and its ability to compute
recirculation cases with wind forcing.

Analysis of PDEs;Classical Physics