= Wind-driven circulation over parabolic basin topography
{title2=$H=ax(L_x-x)$}
With $f=f_0+\beta y$ and parabolic depth, the <topographic potential-vorticity pseudovelocity> is $(-\beta/H,-fH_x/H^2)$. For positive $f,\beta$, it points west and turns south on the western slope, north on the eastern slope. Its characteristics are the parabolas $y=Qa x(L_x-x)/\beta-f_0/\beta$, where $Q=f/H$. Wind-driven <ocean gyres> are steered by these depth gradients; drag and boundary data determine the actual <ocean transport streamfunction>. The zero-depth shoreline is a singular limit that requires a separate physical regularization.
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