Accuracy of a finite-difference method for computing lake currents

Abstract

A semi-analytic model is used to assess the accuracy of a finite-difference model for computing lake currents. Both models solve the vorticity equation for two-dimensional, time-dependent flow to compute currents in a circular lake with a parabolic depth profile. The semi-analytic solution is obtained by using separation of variables to remove the azimuthal dependence and reduce the equations in cylindrical coordinates to a single equation in two variables, time and radius. This equation is then solved by a finite-difference technique for grid sizes small enough that the solution appears to converge. Comparison with the rectangular finite-difference solution shows a strong improvement in accuracy with decreasing grid size. It is found that about 20 grid points across a lake basin are required to adequately resolve winddriven flow.