A note on the symmetric and antisymmetric constituents of weakly nonlinear solutions of a classical wind-driven ocean circulation model

Abstract

A classical model of wind-driven ocean circulation is studied in the weakly nonlinear approximation. An asymptotic expansion for small Rossby number is applied to the separate symmetric and asymmetric components of the stream function, where the symmetry refers to a north-south reflection transformation. The asymptotic expansion allows for the formulation of a coupled set of nonlinear partial differential equations for the two components. Results show that the asymmetric component is responsible for the formation of steady cyclones and anticyclones that cause the deformation of the total stream function of the system. Higher-order components of the stream function in the asymptotic expansion are forced by an effective wind stress arising from lower-order entries in the Jacobian term, and these effective stresses act only to redistribute vorticity.