Helmholtz's theorems

In fluid mechanics there are several vortex theorems that make statements about the vortex density. Besides Croccos vortex theorem has the following vortex theorems, dealing specifically in inviscid fluids with the temporal and spatial behavior of the vortex density.

Vortex set of Helmholtz

The vortex set of Helmholtz follows from the fact that the field of the vorticity vector is source- free. He says that the flow of the vortex density is constant in space by a vortex tube, ie the circulation does not change along the vortex tube.

Helmholtz also found out that in incompressible fluids, the circulation of the vortex tube is constant. This was generalized by Thomson on barotropic fluids.

Vortex theorem of Thomson

The vortex set of Thomson says that applies to the circulation of barotropic fluids:

This means that the circulation ( frictionless ) barotropic fluids is constant. As a consequence, in currents can inviscid barotropic fluids, which are generated from the idle state, no vortices.