A wetting and drying scheme for POM

In shallow-water models, wetting and drying (WAD) are determined by the total water depth D 1⁄4 0 for ‘dry’ and >0 for ‘wet’. Checks are applied to decide the fate of each cell during model integration. It is shown that with bottom friction values commonly used in coastal models, the shallow-water system may be cast into a Burger’s type equation for D. For flows dominated by D (i.e. jrDj jrH j, where Hðx; yÞ defines topography) a non-linear diffusion equation results, with an effective diffusivity that varies like D, so that ‘dry’ cells are regions where ‘diffusion’ is very small. In this case, the system admits D 1⁄4 0 as part of its continuous solution and no checks are necessary. For general topography, and/or in the case of strong momentum advection, ‘wave-breaking’ solution (i.e. hydraulic jumps and/or bores) can develop. A WAD scheme is proposed and applied to the Princeton Ocean Model (POM). The scheme defines ‘dry’ cells as regions with a thin film of fluid O (cm). The primitive equations are solved in the thin film as well as in other regular wet cells. The scheme requires only flux-blocking conditions across cells’ interfaces when wet cells become dry, while ‘dry’ cells are temporarily dormant and are dynamically activated through mass and momentum conservation. The scheme is verified against the above-mentioned diffusion and Burger’s type equations, and tested also for one and two-dimensional channel flows that contain hydraulic jumps, including a laboratory dam-break problem. 2004 Published by Elsevier Ltd.