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arXiv · 1112.0966

Dynamics of helical vortices and helical-vortex rings

E. B. Sonin
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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.

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E. B. Sonin. 2011-12-05. Dynamics of helical vortices and helical-vortex rings. https://doi.org/10.1209/0295-5075%2F97%2F46002

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