What is "vorticity"

n. (context mathematics fluid dynamics English) A property of a fluid flow related to local angular rotation; defined as the curl of the flow's velocity field.

In continuum mechanics, the vorticity is a pseudovector field that describes the local spinning motion of a continuum near some point (the tendency of something to rotate ), as would be seen by an observer located at that point and traveling along with the flow.

Conceptually, vorticity could be determined by marking the part of continuum in a small neighborhood of the point in question, and watching their relative displacements as they move along the flow. The vorticity vector would be twice the mean angular velocity vector of those particles relative to their center of mass, oriented according to the right-hand rule. This quantity must not be confused with the angular velocity of the particles relative to some other point.

More precisely, the vorticity is a pseudovector field , defined as the curl (rotational) of the flow velocity vector. The definition can be expressed by the vector analysis formula:

ω⃗ ≡ ∇ × u⃗ , 

where ∇ is the del operator. The vorticity of a two-dimensional flow is always perpendicular to the plane of the flow, and therefore can be considered a scalar field.

The vorticity is related to the flow's circulation (line integral of the velocity) along a closed path by the (classical) Stokes' theorem. Namely, for any infinitesimal surface element C with normal direction and area dA, the circulation dΓ along the perimeter of C is the dot product ∙ (dA ) where is the vorticity at the center of C.

Many phenomena, such as the blowing out of a candle by a puff of air, are more readily explained in terms of vorticity rather than the basic concepts of pressure and velocity. This applies, in particular, to the formation and motion of vortex rings.