The equatorial Kelvin wave in finite difference models

Abstract

Coarse resolution ocean models tend to poorly resolve many smaller‐scale phenomena, including the equatorial currents narrowly confined around the equator. We study the free equatorial Kelvin wave in inviscid finite difference models using the Arakawa A, B, C, and E grids. Exact analytic solutions with meridional velocity ν = 0 are found on the A, C, and E grids. As the assumption ν = 0 is not valid on the B grid, the solution is obtained numerically by a “shooting” method. In all cases, the wave remains nondispersive, and the phase speed is unchanged from that in the continuum except in the B grid, where it decreases with worsening resolution. The mean zonal heat transport by the Kelvin wave during an El Niño is compared on the various grids. In terms of the currents and sea level displacements, the B grid best models the equatorial Kelvin wave under coarse resolution, though in terms of zonal heat transport and phase velocity, the C grid appears superior. The A and E grids appear to have the most trouble. Our theoretical predictions are checked experimentally by generating equatorial Kelvin waves in linear shallow‐water equation models on the various grids. Additional effects of Rayleigh damping and Newtonian cooling are studied in the appendix.