A generalization of vortex lines
Abstract
Helmholtz theorem states that, in ideal fluid, vortex lines move with the fluid. Another Helmholtz theorem adds that strength of a vortex tube is constant along the tube. The lines may be regarded as integral surfaces of a 1dimensional integrable distribution (given by the vorticity 2form). In general setting of theory of integral invariants, due to Poincare and Cartan, one can find $d$dimensional integrable distribution whose integral surfaces show both properties of vortex lines: they move with (abstract) fluid and, for appropriate generalization of vortex tube, strength of the latter is constant along the tube.
 Publication:

arXiv eprints
 Pub Date:
 March 2016
 arXiv:
 arXiv:1603.09563
 Bibcode:
 2016arXiv160309563F
 Keywords:

 Mathematical Physics;
 Physics  Fluid Dynamics
 EPrint:
 8 pages, 3 figures