Coriolis parameter ($f$)

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.

An inertial oscillation is the horizontal circular motion of an unforced parcel in a rotating fluid. On an f-plane, $\dot{u}-fv=0$ and $\dot{v}+fu=0$, so the speed is constant and the angular frequency is $|f|$.

On a beta plane, the turning rate of an inertial oscillation is larger on the poleward side of its orbit than on the equatorward side. For initial speed $V$ and $\beta V/f_0^2\ll 1$, this asymmetry produces westward mean drift of magnitude $\beta V^2/(2f_0^2)$.