Discussion
Which relation gives the geostrophic vorticity in terms of geopotential?
Answer: C
Taking the curl of the geostrophic wind gives the relative vorticity as \( \nabla^{2}\Phi / f \), so a low is a region of positive geostrophic vorticity in the northern hemisphere. This is why the height field alone determines the vorticity in balanced flow, and it is the basis of potential vorticity inversion. The result also explains why sharp troughs, with strongly curved contours, correspond to large vorticity maxima. Working one numerical case through both cases side by side fixes the distinction better than any rule of thumb.
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