Barotropic vorticity equation

From Glossary of Meteorology

barotropic vorticity equation

The vorticity equation in the absence of horizontal divergence and vertical motion, so that the absolute vorticity of a parcel is materially conserved,
where ζ is the relative vorticity, and f the Coriolis parameter.

This equation may also be interpreted as governing vertically averaged flow in which divergence is present but wind direction is constant with height.
See also equivalent barotropic model.