Dynamics of helical vortices and helical-vortex rings

Details Dynamics of helical vortices and helical-vortex rings Dynamics of helical vortices and helical-vortex rings

2011-12-05

arxiv.org/abs/1112.0966v1

Europhys. Lett. 97, 46002 (2012)

Physics

Condensed Matter

Other Condensed Matter

6 pages, 4 figures

Scientific paper

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.

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