Inertial oscillation

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 $\beta V^2/(2f_0^2)$.