Quasi-geostrophic equations

Geostrophic ow means a stationary ow where the Coriolis force is balanced by the pressure gradient. This has several implications

• the flow is stationary,
• any flow that satisfies the geostrophic momentum equations also satisfies exactly the continuity equation,
• the horizontal flow is vertically independent,
• no divergent or convergent flow is allowed.

Consider the horizontal momentum equations for an inviscid uid under the beta plane approximation. Also, the flow is nearly geostrophic, but not quite, so we will consider the full equations

$\frac{D\,u}{Dt} - f\,v = -\frac{1}{\rho}\frac{\partial p}{\partial x}$