ON THE APPROXIMATION OF HORIZONTAL GRADIENTS IN SIGMA COORDINATES FORBATHYMETRY WITH STEEP BOTTOM SLOPES

Nowadays the simulation of free surface flow and transport in rivers, estuaries and seas is often based upon three-dimensional modelling sys tems. Most of these three-dimensional modelling systems use sigma co-o rdinates in the vertical. By the use of the sigma transformation the w ater column can be divided into the same number of layers independentl y of the water depth. Especially for steep bottom slopes combined with vertical stratification of the density, sigma-transformed grids impos e numerical problems for the accurate approximation of horizontal grad ients. This paper deals with algorithms for the approximation in sigma co-ordinates of the horizontal diffusive fluxes of temperature and sa linity and for the approximation of the horizontal pressure gradients. The approximation of the horizontal diffusive fluxes is based upon a finite volume method. The approximation of the pressure gradients is d irectly related to the approximation of the diffusive fluxes. Artifici al vertical diffusion and artificial flow due to truncation errors are minimized. The method described in this paper is not hampered by the so-called 'hydrostatic consistency condition'. This will be illustrate d by numerical experiments.