The use of a discrete vortex model for shallow water flow around islands and coastal structures

Abstract

A numerical method for solving the depth integrated flow equations (shallow water equations) at high Reynolds numbers is presented. When introducing a depth integrated stream function, a depth integrated vorticity field and the rigid lid approximation, it is shown that the flow is fully described by (1) a potential vorticity transport equation and (2) an elliptical flow equation. These equations are solved with a hybrid Eulerian-Lagrangian model using a modified discrete vortex method. The modifications from a pure two-dimensional (2D) discrete vortex method are that the vorticity changes due to depth change and that new vortices are generated not only at the boundaries, but also in areas where bed friction is present. The capabilities of the model are illustrated with simulations of flows through Borda openings and flows around circular islands with different channel cross-sections and varying relative importance of the advective terms and the bed friction terms.