Dynamics of helical vortices and helical-vortex rings

Abstract

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.

6 pages, 4 figures

References in corpus (2)

• Anomalous translational velocity of vortex ring with finite-amplitude Kelvin waves
• Anomalous vortex ring velocities induced by thermally-excited Kelvin waves and counterflow effects in superfluids

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