The deterministic shallow water equations (SWEs) are frequently used as a toy model to verify new techniques supposed to enter the milieu of numerical weather prediction. To combine stochastic and deterministic modeling, we propose a random field whose dynamics are governed by the shallow water formalism. The dynamics are introduced by embedding deterministic velocities into a stochastic tempos...

In this paper, we address the question of the hyperbolicity and the local wellposedness of the two-layer shallow water model, with free surface, in two dimensions. We first provide a general criterion that proves the symmetrizability of this model, which implies hyperbolicity and local well-posedness in Hs(R2), with s > 2. Then, we analyze rigorously the eigenstructure associated to this model ...

We describe the application of a local discontinuous Galerkin method to the numerical solution of the three-dimensional shallow water equations. The shallow water equations are used to model surface water flows where the hydrostatic pressure assumption is valid. The authors recently developed a DGmethod for the depth-integrated shallow water equations. The method described here is an extension ...