Anticyclonic gradient-wind branches
= 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 $V_\pm=fr[1\pm\sqrt{1-4G/(f^2r)}]/2$. The minus branch approaches the <geostrophic wind> at weak forcing; the plus branch is anomalous. Reality requires $G\le f^2r/4$, so a smooth central pressure maximum must have a radial pressure force vanishing at least linearly toward its centre.