= Spherical potential-vorticity anomaly
{title2=$\psi=Q_0(r^2-3R^2)/6\ (r<R),\quad\psi=-Q_0R^3/(3r)\ (r>R)$}
A uniform positive <quasi-geostrophic potential vorticity> anomaly in a sphere of stretched radius $R$ has the displayed regular, decaying <streamfunction>. Both it and its radial derivative match at the sphere. In its equatorial plane the horizontal <relative vorticity> is $2Q_0/3$ inside and $-Q_0R^3/(3r^3)$ outside. The exterior potential-vorticity anomaly remains zero because its vertical stretching contribution compensates that <relative vorticity>. A stretched sphere corresponds to a flattened ellipsoid in physical coordinates when $N\gg|f|$.
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