Bryan, K., and M. D. Cox, 1968: A nonlinear model of an ocean driven by wind and differential heating: Part II. An analysis of the hear, vorticity and energy balance. Journal of the Atmospheric Sciences, 25 (6), 968-978.

Abstract: An analysis is made of the heat and vorticity balance of a numerical model of a baroclinic ocean. The computation is carried out on a three-dimensional grid designed to resolve the thermocline, and the narrow sidewall boundary layers at the coasts. A vorticity analysis indicates almost perfect geostrophic balance in the interior. In the immediate vicinity of the western wall the vorticity balance at a given level is dominated by lateral friction and vortex stretching associated with upwelling. The "beta" effect plays an important, but somewhat lesser role. A study of the heat balance in the interior shows that lateral advection is of primary importance in the upper part of the model ocean as it removes heat received at the surface in areas of wind-induced downwelling. Some of this heat is carried to the western boundary where is compensates the cooling due to upwelling and convective transfer through the surface.
An examination of the time-dependent motion indicates a regular downstream movement of eddies in the western boundary current. These eddies extend throughout the water column and give rise to a Reynolds stress which acts to retard the time-averaged flow. In a test run with bottom friction included, these eddies are slowly damped.