Two-dimensional shallow flow equations for partially dry areas

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