A two-layer frictional model of wind-driven motion in a rectangular oceanic basin

A study is made of the circulation in a two-layer ocean with rectangular boundaries driven by a zonal wind stress. The dynamics is linear, with bottom and interface stresses. A non-linearity arises from finite variations in layer depths. In the case where the lower layer is much deeper than the upper layer the equations can be integrated exactly. The solution gives a directly wind-driven gyre in the upper layer, with an interior Sverdrup regime and a western boundary current. In the lower layer there is no interior motion but a recirculating boundary current develops. The total transport is thereby intensified near the coast while a counter-transport develops at the outer edge. The boundary current width varies with the current depth and the latitude.

The key parameter in the model is ε = (D/F)(H/h₀), where D and F are the “frictional depths” applicable at the interface and the bottom, H and h₀ are the total depth and the upper layer depth. Numerical examples are worked out for a sinusoidal wind stress distribution in the case ε = 1.