On parametric values and types of representation in wind-driven ocean circulation studies

Abstract

The vertically averaged equations of motion for the barotropic model of wind-driven ocean circulation on the β-plane are discussed. An attempt is made to evaluate the two non-dimensional parameters, viz., the Rossby number, R, and the (bottom) frictional parameter, ?, by comparing observed scales with those derived from simple boundary layer arguments. It is found that ? and R are (upper) bounded for the model if one imposes the scale of the Gulf Stream as the smallest significant scale of the ocean. Maximum values for the bottom-friction coefficient and for the ratio of wind-stress to depth of the model are determined. The general problem of analyzing the equations by approximate (numerical) techniques is discussed and a proposal is made to carry out the analysis by working with limited representations and correspondingly exaggerated values of the parameters. Finally a comparison is made of the error involved in treating Stommel's steady, linear, frictional model by two approximate methods, a limited Fourier representation and a finite-difference scheme. The latter is found to describe the solution of the linear model with considerably less distortion than the former. Flans to treat the fully non-linear, time-dependent system are described. DOI: 10.1111/j.2153-3490.1965.tb00196.x