# A CONTINUOUSLY STRATIFIED THERMOCLINE MODEL INCORPORATING A MIXED LAYER OF VARIABLE THICKNESS AND DENSITY.

(MARSHALL, JC and NURSER, AJG), *JOURNAL OF PHYSICAL OCEANOGRAPHY*, vol. 21, no. 12, pp. pages, 1991.

## Abstract

A continuously stratified, steady thermocline model is formulated in which a mixed layer of variable depth and density overlies a stratified thermocline. Rather than prescribe the distribution of density and vertical velocity at the top of the permanent thermocline, we explicitly represent the dynamics of the vertically homogeneous layer that overlies it; the density distribution at the sea surface, the depth of the mixed layer, and the structure of the thermocline are all found for prescribed patterns of Ekman pumping and surface buoyancy fluxes. If the potential vorticity of the thermocline is assumed to have a uniform value on isopycnal surfaces, it is shown that the problem can be reduced to one of finding the distribution of a single scalar field, the mixed-layer density, by the method of characteristics. Given this field and knowledge of the potential vorticity distribution in the thermocline, all other variables of the model can be found. The resulting model seems ideally suited to the study of the interaction of a mixed layer with a stratified thermocline, since it explicitly represents the lateral geostrophic flow through the sloping base of the mixed layer. Idealized solutions are presented for both subtropical and subpolar gyres in which, in response to patterns of wind and diabatic forcing, isopycnals outcrop into a mixed layer of variable thickness and density. The effect of both warming and cooling of the mixed layer on the structure of gyre is investigated.