Wind stress curl ($({\nabla }_h\times \mathbf{\tau }{)}_z$)

The vertical curl of surface wind stress is $({\nabla }_h\times \mathbf{\tau }{)}_z={\tau }_{y,x}-{\tau }_{x,y}$. In a layer of density ${\rho }_0$ and depth $h$, its normalized potential vorticity source is $W=({\nabla }_h\times \mathbf{\tau }{)}_z/({\rho }_{0}h)$. It drives Sverdrup balance in the weakly nonlinear steady ocean interior.