Consider eastward flow at uniform speed \(U\) over a step change in depth (at \(x = 0\)) running north–south, across which the layer thickness changes discontinuously from \(h_0\) to \(h_1\). The flow upstream of the step has no relative vorticity. To conserve the ratio $(\zeta + f)/h$, the flow must suddenly acquire negative (clockwise) relative vorticity due to the sudden decrease in layer thickness. The relative vorticity of a fluid element just after passing the step can be found from \[ \frac{f}{h_0} = \frac{(\zeta + f)}{h_1} \Rightarrow \zeta = \frac{f(h_1 - h_0)}{h_0} < 0 \] where \(f\) is evaluated at the upstream latitude of the streamline

A westward one feels the upstream influence of the step so that it acquires a counterclockwise curvature before it encounters the step. The positive vorticity is balanced by a reduction in \(f\), which is consistent with conservation of potential vorticity. At the location of the step the vorticity decreases suddenly. Finally, far downstream of the step the fluid particle is again moving westward at its original latitude. The westward flow over a topographic step is not oscillatory.