Physical interpretation for geophysical flows.

Geophysical flows typically have small $U$ and large vertical scale $H$, so $gH/U^2$ is very large and $\mathrm{Fr}=\dfrac{U}{\sqrt{gH}}\ll 1$. Thus $\mathrm{Fr}^2\ll 1$ and the advective term is small compared with the hydrostatic pressure-gradient; the leading balance is hydrostatic (pressure gradient balances gravity), and vertical accelerations are negligible. Using the numerical hint $U\sim 0.1\ \mathrm{m/s}$, for a depth $H$ of order $10^2\!-\!10^3\ \mathrm{m}$ one finds $\mathrm{Fr}^2$ extremely small and pressure/hydrostatic forces dominate inertial advective effects. In other words, geophysical flows are often (nearly) hydrostatic.