= Circular topographic anticyclone
{title2=$q=-f\epsilon\,\mathbf1_{r<a}$}
For an upstream irrotational current on an <f-plane> in a rigid layer of height $h$, a circular region of height $h(1-\epsilon)$ has the displayed relative <vorticity> if its fluid retains upstream <potential vorticity> $f/h$. To leading order in the height contrast, take $u=-\Psi_y$, $v=\Psi_x$ and $\Psi=-Uy+\psi$. Solving the <Poisson equation> for $\psi$ gives $\psi=-Cr^2/2$ inside and $\psi=Ca^2[\log(a/r)-1/2]$ outside, where $C=f\epsilon/2$. The disturbance is clockwise for positive $f\epsilon$. Variable-depth transport and the transition across the rim introduce higher-order corrections to this leading columnar inversion.
Back to article page
