Layer-averaged Euler and Navier-Stokes equations

M. -O. Bristeau, C. Guichard, B. Di Martino, J. Sainte-Marie

Published 2015-09-21Version 1

In this paper we propose a strategy to approximate incompressible 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.