| Abstract: | A 3D semi-implicit finite volume scheme for shallow- water flow with the hydrostatic pressure assumption has been developed using the σ-co-ordinate system, incorporating a standard k–ε turbulence transport model and variable density solute transport with the Boussinesq approximation for the resulting horizontal pressure gradients. The mesh spacing in the vertical direction varies parabolically to give fine resolution near the bed and free surface to resolve high gradients of velocity, k and ε. In this study, wall functions are used at the bed (defined by the bed roughness) and wind stress at the surface is not considered. Surface elevation gradient terms and vertical diffusion terms are handled implicitly and horizontal diffusion and source terms explicitly, including the Boussinesq pressure gradient term due to the horizontal density gradient. The advection terms are handled in explicit (conservative) form using linear upwind interpolation giving second-order accuracy. A fully coupled solution for the flow field is obtained by substi- tuting for velocity in the depth-integrated continuity equation and solving for surface elevation using a conjugate gradient equation solver. Evaluation of horizontal gradients in the σ-co-ordinate system requires high-order derivatives which can cause spurious flows and this is avoided by obtaining these gradients in real space. In this paper the method is applied to parallel oscillatory (tidal) flow in deep and shallow water and compared with field measurements. It is then applied to current flow about a conical island of small side slope where vortex shedding occurs and velocities are compared with data from the laboratory. Computed concentration distributions are also compared with dye visualization and an example of the influence of temperature on plume dispersion is presented. © 1997 John Wiley & Sons, Ltd. |
