Dynamics of helical vortices and helical-vortex rings
Racah Institute of Physics, Hebrew University of Jerusalem - Jerusalem 91904, Israel
Accepted: 9 January 2012
The letter considers dynamics of helical vortices and helical-vortex rings either solving directly the equations of motions of a vortex line or using canonical relations following from the Hamiltonian equations of motion. An analytical solution in elliptical integrals was found for helical-vortex rings in the local-induction approximation. The analysis based on the canonical Hamilton relation provides a clear physical explanation for anomalous velocities of helical-vortex rings, i.e., for suppression of the velocity and even inversion of its direction at sufficiently large amplitude of the helical distortion. The extended local-induction approximation is suggested, which provides an exact solution for the equations of motion of helical vortices and helical-vortex rings in the limit when the small-pitch helical vortex reduces to a cylindric sheet of uniform vorticity.
PACS: 67.25.dk – Vortices and turbulence / 47.32.cf – Vortex reconnection and rings / 67.30.he – Textures and vortices
© EPLA, 2012