A wetting and drying scheme for POM

In shallow-water models, wetting and drying (WAD) are determined by the total water depth D ¼ 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. jrD jj r H j, where H ðx; yÞ 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 ¼ 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.

[1]  J. C. Jaeger,et al.  Conduction of Heat in Solids , 1952 .

[2]  R. D. Richtmyer,et al.  Difference methods for initial-value problems , 1959 .

[3]  G. Mellor.  USERS GUIDE for A THREE-DIMENSIONAL, PRIMITIVE EQUATION, NUMERICAL OCEAN MODEL , 1998 .

[4]  A. Balzano,et al.  Evaluation of methods for numerical simulation of wetting and drying in shallow water flow models , 1998 .

[5]  L. Oey,et al.  Assimilation of drifter and satellite data in a model of the Northeastern Gulf of Mexico , 2004 .

[6]  Guus S. Stelling,et al.  Practical Aspects of Accurate Tidal Computations , 1986 .

[7]  Guus S. Stelling,et al.  A staggered conservative scheme for every Froude number in rapidly varied shallow water flows , 2003 .

[8]  Hyun-chul Lee,et al.  The variability of currents in the Yucatan Channel: Analysis of results from a numerical ocean model , 2003 .

[9]  Walter R. Johnson,et al.  A Model of the Near-Surface Circulation of the Santa Barbara Channel: Comparison with Observations and Dynamical Interpretations , 2004 .

[10]  L. Oey,et al.  Near-Surface Currents in DeSoto Canyon (1997–99): Comparison of Current Meters, Satellite Observation, and Model Simulation , 2003 .

[11]  Lie-Yauw Oey,et al.  The generation of subsurface cyclones and jets through eddy-slope interaction , 2004 .

[12]  Hyun-chul Lee,et al.  Effects of winds and Caribbean eddies on the frequency of Loop Current eddy shedding: A numerical model study , 2003 .

[13]  Lie-Yauw Oey,et al.  Deep Eddy Energy and Topographic Rossby Waves in the Gulf of Mexico , 2002 .

[14]  L. Oey.  Simulation of Mesoscale Variability in the Gulf of Mexico: Sensitivity Studies, Comparison with Observations, and Trapped Wave Propagation , 1996 .

[15]  Alan M. Davies,et al.  Modeling Marine Systems , 1989 .

[16]  G. Mellor.  The Three-Dimensional Current and Surface Wave Equations , 2003 .

[17]  George L. Mellor,et al.  A Three-Dimensional Simulation of the Hudson Raritan Estuary. Part I: Description of the Model and Model Simulations , 1985 .

[18]  M. R. Morton,et al.  Wetting and drying simulation of estuarine processes , 2001 .

[19]  R. T. Cheng,et al.  SEMI-IMPLICIT FINITE DIFFERENCE METHODS FOR THREE-DIMENSIONAL SHALLOW WATER FLOW , 1992 .

[20]  P. Smolarkiewicz.  A Fully Multidimensional Positive Definite Advection Transport Algorithm with Small Implicit Diffusion , 1984 .

[21]  H. S. Carslow,et al.  Conduction of Heat in Solids, Second Edition , 1986 .