Two-dimensional shallow flow equations for partially dry areas

A new set of two-dimensional shallow flow equations is developed in order to deal with partially wet and very irregular domains. The bottom irregularities, which in many practical cases strongly affect the dynamics and the continuity, are accounted for statistically. Assuming hydrostatic approximation, the three-dimensional Reynolds equations are suitably averaged over a representative elementary area and then integrated over the depth. The resulting subgrid model for ground irregularities is tested by resolving two sample problems. The first concerns the wetting and drying of tidal flats; the second deals with overland flow on an irregular plane surface. Numerical simulations show that the proposed equations are a useful tool for modelers who have to cope with partially dry domains.