Vorticity

vorticity

A vector measure of local rotation in a fluid flow, defined mathematically as the curl of the velocity vector,

where ζ is the vorticity, u the velocity, and ∇ the del operator.

The vorticity component normal to a small plane element is the limit of the circulation per unit area as the area of the element approaches zero (see Stokes's theorem). The vorticity of a solid rotation is twice the angular velocity vector. In meteorology, "the vorticity" usually refers to the vertical component of the vorticity.
See also relative vorticity, absolute vorticity, geostrophic vorticity, thermal vorticity, vorticity equation, curl;
compare deformation, divergence.