An Eddifying Parsons Model

Abstract

The time-mean effects of eddies are studied in a model based on the Parsons–Veronis–Huang–Flierl models of the wind-driven gyre. Much of the analysis used for the steady solutions carries over if the model is cast in terms of the thickness-weighted mean velocity, because then mass transport is nondivergent in the absence of diabatic forcing. The model exemplifies the use of residual mean theory to simplify analysis.

A result of the analysis is a boundary layer width in the case of a rapid upper-layer flow and weak lower-layer flow. This boundary layer width is comparable to an eddy mixing length when the typical eddy velocity is taken to be the long Rossby wave phase speed.

Further analysis of the model illustrates important aspects of eddy behavior, model sensitivity to eddy fluxes, and model sensitivity to frictional parameters.