Rossby Wave Frequencies and Group Velocities for Finite Element and Finite Difference Approximations to the Vorticity-Divergence and the Primitive Forms of the Shallow Water Equations

Abstract

In this paper Rossby wave frequencies and group velocities are analyzed for various finite element and finite difference approximations to the vorticity-divergence form of the shallow water equations. Also included are finite difference solutions for the primitive equations for the staggered grids B and C from Wajsowicz and for the unstaggered grid A. The results are presented for three ratios between the grid size and the Rossby radius of deformation. The Yortcity-divergence equation schemes give superior solutions to those based on the primitive equations. The best results come from the finite element schemes that use linear basis functions on isosceles triangles and bilinear functions on rectangles. All of the primitive equation finite difference schemes have problems for at least one Rossby deformation-grid size ratio.