Vorticity

Vorticity is the curl of the velocity field, omega = grad cross v, measuring the local spin of fluid elements. In rotating geophysical flow the vertical component matters most: relative vorticity zeta plus the planetary vorticity f gives absolute vorticity, and dividing by layer thickness gives potential vorticity, conserved following the flow in the absence of friction and forcing. The beta effect, the meridional change of f, is central to Rossby-wave propagation and western intensification. Vorticity dynamics, not the velocity field directly, organize large-scale ocean and atmospheric circulation.