  We propose a multi-layer approach to simulate hyperpycnal and hypopycnal
plumes in flows with free surface. The model allows to compute the vertical
profile of the horizontal and the vertical components of the velocity of the
fluid flow. The model can describe as well the vertical profile of the sediment
concentration and the velocity components of each one of the sediment species
that form the turbidity current. To do so, it takes into account the settling
velocity of the particles and their interaction with the fluid. This allows to
better describe the phenomena than a single layer approach. It is in better
agreement with the physics of the problem and gives promising results. The
numerical simulation is carried out by rewriting the multi-layer approach in a
compact formulation, which corresponds to a system with non-conservative
products, and using path-conservative numerical scheme. Numerical results are
presented in order to show the potential of the model.
