Three-Dimensional Boundary-Fitted Circulation Model

Abstract

A spherical coordinate, three-dimensional, nonorthogonal, boundary-fitted circulation model (contravariant formulation) for application to estuarine, coastal sea, and continental shelf waters is presented. The model employs a split mode technique where the equations are decomposed into exterior and interior modes. The exterior mode (vertically averaged) described in an earlier paper (Muin and Spaulding 1996) is solved using a semiimplicit solution technique. The interior mode (vertical structure) is solved explicitly, except for the vertical diffusion terms that are solved implicitly. The temporally and spatially varying eddy viscosity and diffusivity are determined from a turbulent kinetic energy equation and an empirically specified length scale. A series of tests are presented to evaluate model performance where analytical solutions or other numerical solutions are available for comparison. The model's ability to predict the point vertical structure of tidal flow is tested against analytic solutions employing (1) constant viscosity; and (2) an eddy viscosity varying linearly with depth with a no-slip bottom boundary condition. The ability of the model to simulate three-dimensional tidal flow was tested against an exact solution for an annular section channel with quadratically varying bathymetry. The model was also tested against analytic solutions for steady residual flow generated by density gradient, wind, and river flow in a channel. The model predicted turbulent energy distributions generated from a bottom boundary were compared to those from a previous numerical study by Davies and Jones (1990). No-slip and bottom stress formulations at the sea bed, and their effect on the vertical structure of the flow are analyzed. The model was used to predict the salinity distribution in a simple rectangular channel identical to the Rotterdam Waterway. The computational method is very economical, stable, and accurate with the CFL stability condition up to 100.