Article ID Journal Published Year Pages File Type
8255729 Journal of Geometry and Physics 2018 22 Pages PDF
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.
Related Topics
Physical Sciences and Engineering Mathematics Mathematical Physics
Authors
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