A new well-posed vorticity divergence formulation of the shallow water equations

Abstract

A completely new vorticity-divergence formulation of the two-dimensional shallow water equations including boundary conditions is derived. The new formulation is necessary since the conventional one does not lead to a well-posed initial boundary value problem for limited area modelling.The new vorticity-divergence formulation include four dependent variables instead of three, and require more equations and boundary conditions than the conventional formulation. On the other hand, it forms a symmetrizable hyperbolic set of equations with well defined boundary conditions that leads to a well-posed problem with a bounded energy.