On the Relationship between Subduction Rates and Diabatic Forcing of the Mixed Layer

Abstract

The transport of mass between a mixed layer, exposed to mechanical and thermodynamic forcing, and an adiabatic thermocline is studied for gyre-scale motions. It is shown that if the mixed layer can be represented by a vertically homogeneous layer, whose base velocity and potential density are continuous, then, at any instant, the rate at which fluid is subducted per unit area of the sloping mixed-layer base, S, is given bywhere h is the depth of the mixed layer, Qb = ?f???1??/?z|z?h is th large-scale potential vorticity is the base, ?net is the heat input per unit area less that which warms the Ekman drift, αE, Cw, and ?? are the volume expansion coefficient, heat capacity, and mean density of water, respectively. It is assumed that the mixed layer is convectively controlled and much deeper than the layer directly stirred by the wind. The field of S is studied in a steady thermocline model in which patterns of Ekman pumping and diabatic heating drive flow to and from a mixed layer overlying a stratified thermocline.