Abstract
A flux form of the Potential vorticity (PV) equation is applied to study the creation and transport of potential vorticity in an ocean gyre; generalized PV fluxes (J vectors) and the associated PV flux fines are used to map the creation, by buoyancy forcing, of PV in the mixed layer and its transport as fluid is subducted through the base of the mixed layer into the thermocline. The PV flux lines can either close on themselves (recirculation) or begin and end on the boundaries (ventilation). Idealized thermocline solutions are diagnosed using J vectors, which vividly illustrate the competing process of recirculation through western boundary currants and subduction from the surface.
Potential vorticity flux vectors are then used to quantify the flux of mass passing invisidly through a surface across which potential vorticity changes discontinuously but at which potential density and velocity are continuous. Such a surface might be the base of the oceanic mixed layer or, in a meteorological context, the tropopause. It is shown that, at any instant, the normal flux of fluid per unit area across such a surface is given, very generally, bywhere u is the velocity and n is the normal vector to the surface. Here ω is the absolute vorticity; B = −gDσ/Dt is the buoyancy forcing, with D/Dt the substantial derivative and σ the potential density; Q = −ρ−1ω·∇σ is the potential vorticity; ρ the in situ density., and g the gravitational acceleration. Square brackets denote the change in the enclosed quantity across the surface.
