Vorticity

Summary

Vorticity is the curl of the velocity field of a flow, $\boldsymbol{\omega} = \nabla \times \mathbf{u}$. It measures the local rate of rotation of the fluid: a small parcel spins with angular velocity $\boldsymbol{\omega}/2$. Flows with zero vorticity are called irrotational, and vorticity is the key quantity in the study of vortices and turbulence.