Fluid flow on a rotating body for which the Rossby number and Ekman number satisfy
so that the Navier-Stokes equations for a rotating fluid become
The Coriolis force is always perpendicular to the direction of flow (to the right in the northern hemisphere and to the left in the southern hemisphere), so the pressure gradient is also perpendicular to the flow. This requires that the pressure be constant along a streamline.
Taking the curl of both sides of the geostrophic equation yields the Taylor-Proudman theorem.
Ekman Number, Geostrophic Equation, Navier-Stokes Equations--Rotational, Rossby Number, Taylor-Proudman Theorem
