A Numerical Approach to Equatorial Oceanic Wave-Mean Flow Interactions

Abstract

An efficient numerical method is employed to investigate the interaction of equatorial trapped waves with vertically and meridionally sheared zonal jets. The model is formulated with the Equatorial Undercurrent in mind but has general applicability. The governing differential equation is derived and expanded using central differences into finite difference form. The linear system of equations leads to a coefficient matrix of block-tridiagonal form which is efficiently solved using a direct method. The direct method involves an optimized Gauss elimination and backsubstitution. For long Kelvin waves in the absence of mean flow, the analytic solution is obtained numerically with a high degree of accuracy. A diagnostic test is derived for use in cases where the analytic solution is unknown. The model is then applied to situations in which waves are superimposed on a background flow containing a critical surface where the flow speed matches the phase speed of the wave. For these cases, the waves are damped and absorbed in a frictional layer surrounding the critical surface. For speeds characteristic of the Undercurrent, all but the first few baroclinic Kelvin modes encounter critical surfaces which may prevent the establishment of higher baro-clinic modes in the equatorial ocean.