Rotating fluid

A rotating fluid is described in a rotating reference frame, where the Coriolis acceleration and centrifugal acceleration supplement the physical forces.

The Coriolis parameter is $f=2\Omega \sin \phi$ for planetary rotation rate $\Omega$ and latitude $\phi$. It controls the vertical component of the Coriolis acceleration acting on horizontal flow.

An f-plane approximates the Coriolis parameter by a constant $f_0$ over a limited horizontal region.

A beta plane retains the leading meridional variation $f=f_0+\beta y$ of the Coriolis parameter.

Potential vorticity combines fluid rotation with stretching and stratification. For an inviscid barotropic shallow-water layer,where $\zeta$ is relative vorticity and $h$ is layer thickness.

Shallow-water potential vorticity is materially conserved by inviscid, unforced shallow water equations. Linearizing about rest with depth $H_0$ gives an anomaly proportional to