Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8255729 | Journal of Geometry and Physics | 2018 | 22 Pages |
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 1-dimensional integrable distribution (given by the vorticity 2-form). In general setting of theory of integral invariants, due to Poincaré and Cartan, one can find d-dimensional integrable distribution (given by a possibly higher-rank form) 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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
M. Fecko,