= Gaussian topographic response with compensated uniform potential vorticity
{c}
{title2=$\psi'=f\epsilon a^2e^{-r^2/a^2}/H$}
In a shallow-water <potential-vorticity inversion> with the background gradient explicitly compensated, uniform PV gives $(\nabla^2-L_R^{-2})\psi'=-fb/H$. The displayed <Gaussian function> solves it for $b=\epsilon[4(1-r^2/a^2)+a^2/L_R^2]e^{-r^2/a^2}$. This is not, without that compensation, a steady solution of the standard finite-depth constant-f current problem: its residual is $U\psi'_x/L_R^2$. Closed streamlines can occur while <Rossby number> and surface displacement remain small.
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