On the Wind-Driven Ocean Circulation

Abstract

Some aspects of existing theories of the wind-driven ocean circulation are examined with particular emphasis on the question of the need for the inclusion of lateral eddy viscosity to provide a mechanism for balancing the applied wind torque. A new model is proposed according to which the ocean is divided into a southern and a northern portion, attention being restricted to the former which is itself subdivided into an interior region and a boundary region adjacent to the western shore. The equations of motion in terms of spherical coordinates are formally integrated over depth for both a homogeneous and a two-layer ocean. Approximate equations analogous to those used in existing theories are proposed for the interior region. Conditions in the boundary region are considered in an effort to determine the relative importance of the various terms in the equations. Based on these considerations approximate equations are derived for the boundary region. These imply the predominance of the pressure terms, the nonlinear inertia terms and the terms arising from the variation of the Coriolis parameter with latitude.
 The approximate equations are transformed to surface coordinates and are applied to the homogeneous ocean and a two-layer ocean subjected to a simple wind distribution, yielding reasonable results. It is shown that the variation of the Coriolis parameter plays a fundamental role in the formation of the stream on the western shore. Simple physical interpretations of the results are presented including an explanation of the facts that no similar stream can be formed on the eastern shore and that the variation of depth in a two-layer ocean, when the Coriolis parameter is assumed constant, cannot give rise to an intense stream. Appropriate curves illustrating the dependence of the solutions on certain dimensionless parameters are given. When applied to the North Atlantic the theory gives reasonable results for the Gulf Stream north to, say, Cape Hatteras.