A SEMIIMPLICIT LAGRANGIAN SCHEME FOR 3D SHALLOW-WATER FLOW WITH A 2-LAYER TURBULENCE MODEL

A semi-implicit Lagrangian finite difference scheme for 3D shallow wat er flow has been developed to include an eddy viscosity model for turb ulent mixing in the vertical direction. The a-co-ordinate system for t he vertical direction has been introduced to give accurate definition of bed and surface boundary conditions. The simple two-layer mixing le ngth model for rough surfaces is used with the standard assumption tha t the shear stress across the wall region at a given horizontal locati on is constant. The bed condition is thus defined only by its roughnes s height (avoiding the need for a friction formula relating to depth-a veraged flow, e.g. Chezy, used previously). The method is shown to be efficient and stable with an explicit Lagrangian formulation for conve ctive terms and terms for surface elevation and vertical mixing handle d implicitly. The method is applied to current flow around a circular island with gently sloping sides which produce periodic recirculation zones (vortex shedding). Comparisons are made with experimental measur ements of velocity using laser Doppler anemometry (time histories at s pecific points) and surface particle-tracking velocimetry.