Abstract
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 Poincare 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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
