text: A vortex line or vorticity line is a line which is everywhere tangent to the local vorticity vector. Vortex lines are defined by the relation
  where  is the vorticity vector in Cartesian coordinates.
  A vortex tube is the surface in the continuum formed by all vortex lines passing through a given (reducible) closed curve in the continuum. 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 everywhere along the tube (because vorticity has zero divergence). It is a consequence of Helmholtzs theorems (or equivalently, of Kelvins 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 the square of its magnitude) can be intensified when a vortex line is extended — a phenomenon known as vortex stretching. This phenomenon occurs in the formation of a bathtub vortex in outflowing water, and the build-up of a tornado by rising air currents.