Numerical simulation of Rossby wave in shallow water

The semi-implicit, finite volume scheme developed by Sun [13] has been applied to simulate the Rossby waves in the equatorial β-plane discussed by Boyd [1] and [2]. The scheme is simple and flexible, and more accurate than the finite volume, flux-form semi-Lagrangian, Lax–Wendroff scheme, and the others presented in Chu and Fan [3]. Compared with the analytic solution, the scheme with the quadratic upstream interpolation for convective kinetics and Shuman smoothing produces less dispersion than that using the 4th-order advection without smoothing. The results also confirm the perturbation theory that predicts solitary waves of large amplitude containing a region of recirculating fluid trapped within the moving disturbance. The general patterns simulated from the initial zeroth-order solutions and the sum of the zeroth- and first-order solutions remain very similar, although the detail and propagation speed can be different.