The equatorial undercurrent in a two layer shallow water model

A theoretical study of a two layer shallow water equatorial ocean model is presented. We explain why this model which cannot accurately represent the dynamics of the tropical and extratropical areas is able to create a strong equatorial undercurrent, whose dynamics can be explained by a nonlinear mechanism where entrainment plays a prominent role. Under the assumptions that the meridional flow is far weaker than the zonal flow and that the dissipation is negligible, a solution is obtained for the intensity of the equatorial undercurrent as a function of the wind stress and the entrainment. The ratio of these two quantities is shown to define areas of acceleration and decelaration of the equatorial undercurrent. The role of dissipation is also briefly examined. The results are confirmed by numerical experiments made with a two layer model whose first layer has a prescribed depth.