Vertical fluxes of potential vorticity and the structure of the thermocline

A new framework for understanding the vertical structure of ocean gyres is developed based on vertical fluxes of potential vorticity. The key ingredie nt is an integral constraint that in a steady state prohibits a net flux of potential vorticity through any closed contour of Bernoulli potential or d ensity. Applied to an ocean gyre, the vertical fluxes of potential vorticit y associated with advection, friction, and buoyancy forcing must therefore balance in an integral sense. In an anticyclonic subtropical gyre, the advective and frictional potential vorticity fluxes are both directed downward, and buoyancy forcing is requi red to provide the compensating upward potential vorticity flux. Three regi mes are identified: 1) a surface "ventilated thermocline'' in which the upw ard potential vorticity flux is provided by buoyancy forcing within the sur face mixed layer, 2) a region of weak stratification- "mode water'' in whic h all three components of the potential vorticity flux become vanishingly s mall, and 3) an "internal boundary layer thermocline'' at the base of the g yre where the upward potential vorticity flux is provided by the diapycnal mixing. Within a cyclonic subpolar gyre, the advective and frictional poten tial vorticity fluxes are directed upward and downward, respectively, and a re thus able to balance without buoyancy forcing. Geostrophic eddies provide an additional vertical potential vorticity flux associated with slumping of isopycnals in baroclinic instability. Incorpora ting the eddy potential vorticity flux into the integral constraint provide s insights into the role of eddies in maintaining the Antarctic Circumpolar Current and convective chimneys. The possible impact of eddies on the vert ical structure of a wind-driven gyre is discussed.