A wetting and drying scheme for POM

Abstract

In shallow-water models, wetting and drying (WAD) are determined by the total water depth D=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. |∇ D|≫|∇ H|, where H( x, y) defines topography) a non-linear diffusion equation results, with an effective diffusivity that varies like D 2, so that `dry' cells are regions where `diffusion' is very small. In this case, the system admits D=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.