Vorticity

In fluid dynamics, the vorticity is a vector that describes the local spinning motion of a fluid near some point, as would be seen by an observer located at that point and traveling along with the fluid.

Conceptually, the vorticity could be determined by marking the particles of the fluid 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 of a flow is a vector field, equal to the curl (rotational) of its velocity field . It can be expressed by the vector analysis formula, where is the nabla 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 Stokes equation. Namely, for any infinitesimal surface element C with normal direction and area dA, the circulation along the perimeter of C is the dot product 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 vorticty rather than the basic concepts of pressure and velocity. This applies, in particular, to the formation and motion of vortex rings.