 Topographic potential-vorticity pseudovelocity

In the steady small-Rossby number transport equation, this coefficient field advects the ocean transport streamfunction along contours of background shallow-water potential vorticity $f/H$. It is not a physical velocity: when $\psi$ has units of volume transport, its units are inverse length squared per time. For uniform depth on a beta plane it points westward, $\tilde{\mathbf{u}}=(-\beta /H,0)$. With no forcing or drag, $\psi$ is constant on each connected characteristic; locally $\psi =\Phi (f/H)$ at regular points.