Anticyclonic gradient-wind branches

For a conventional Northern-Hemisphere anticyclone let $G=-p_r/\rho >0$. Gradient wind balance gives $V^2/r-fV+G=0$, with $V_{\pm }=fr[1\pm \sqrt{1-4G/(f^{2}r)}]/2$. The minus branch approaches the geostrophic wind at weak forcing; the plus branch is anomalous. Reality requires $G\le f^{2}r/4$, so a smooth central pressure maximum must have a radial pressure force vanishing at least linearly toward its centre.