= Topographic potential-vorticity pseudovelocity
{title2=$\widetilde{\mathbf u}=\widehat{\mathbf z}\times\nabla(f/H)$}
= Pseudovelocity
{synonym}
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, $\widetilde{\mathbf u}=(-\beta/H,0)$. With no forcing or drag, $\psi$ is constant on each connected characteristic; locally $\psi=\Phi(f/H)$ at regular points.
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