Validity criteria for geostrophic balance ($U/(|f|L)\ll 1,(|f|\tau {)}^{-1}\ll 1$)

The Rossby number compares advective acceleration with Coriolis acceleration, and the second ratio compares local time dependence with it. Both should be small when pressure and Coriolis terms dominate horizontal momentum. Surface stress, sharp curvature, small scales, rapid evolution and the near-equatorial region can invalidate the approximation. The vertical hydrostatic equilibrium assumption is a separate scale approximation.