Vorticity - Vortex Lines and Vortex Tubes

Vortex Lines and Vortex Tubes

A vortex line or vorticity line is a line which is everywhere tangent to the local vorticity vector. A vortex tube is the surface in the fluid formed by all vortex-lines passing through a given (reducible) closed curve in the fluid. The 'strength' of a vortex-tube (also called vortex flux) is the integral of the vorticity across a cross-section of the tube, and is the same at everywhere along the tube (because vorticity has zero divergence). It is a consequence of Helmholtz's theorems (or equivalently, of Kelvin's circulation theorem) that in an inviscid fluid the 'strength' of the vortex tube is also constant with time. Viscous effects introduce frictional losses and time dependence.

In a three dimensional flow, vorticity (as measured by the volume integral of its squared magnitude) can be intensified when a vortex-line is extended — a phenomenon known as vortex stretching. This phenomenon occurs in the formation of a bath-tub vortex in out-flowing water, and the build-up of a tornado by rising air-currents.

helicity, which is vorticity in motion along a third axis in a corkscrew fashion.