Geophysical fluid dynamics

Definition

Geophysical fluid dynamics is the study of flows of fluids on a rotating planet, typically the atmosphere and the oceans. The flows are described in a frame that rotates with the planet at angular velocity $\Omega$. In this frame the Navier–Stokes momentum equation is $$\frac{D u}{D t} + 2 \Omega \times u = -\frac{1}{\rho} \nabla p + g + \nu \Delta u.$$ Here $u$ is the velocity relative to the rotating frame, $\rho$ the density and $p$ the pressure. Here $g$ is the effective gravity including the centrifugal force, and $\nu$ is the kinematic viscosity. The subject concerns the regime where the Coriolis term $2 \Omega \times u$ and the buoyancy forces are of leading order. This means a small or moderate Rossby number and a stable stratification.