 Meridional-pressure-gradient geostrophic wind

With $x$ eastward and $y$ northward, a purely meridional pressure gradient gives the velocity in the title. For $f>0$, pressure increasing northward gives westward wind, leaving lower pressure to the wind's left. Reversing the pressure gradient reverses the velocity. At a fixed gradient and density the speed scales as $1/|\sin \varphi |$; the formal equatorial divergence signals breakdown of geostrophic balance, rather than a real infinite wind.