Anomalous translational velocity of vortex ring with finite-amplitude Kelvin waves

Abstract

We consider finite-amplitude Kelvin waves on an inviscid vortex assuming that the vortex core has infinitesimal thickness. By numerically solving the governing Biot-Savart equation of motion, we study how the frequency of the Kelvin waves and the velocity of the perturbed ring depend on the Kelvin wave amplitude. In particular, we show that, if the amplitude of the Kelvin waves is sufficiently large, the perturbed vortex ring moves backwards.

6 pages, 5 figures, v2: minor changes, v3: typos corrected

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Cited by in corpus (18)

• Vortices in Superfluid Films on Curved Surfaces
• Energy cascade with small-scales thermalization, counterflow metastability and anomalous velocity of vortex rings in Fourier-truncated Gross-Pitaevskii equation
• Crossover from interaction to driven regimes in quantum vortex reconnections
• Velocity, energy and helicity of vortex knots and unknots
• Symmetry of Kelvin-wave dynamics and the Kelvin-wave cascade in the T=0 superfluid turbulence
• Dynamics of helical vortices and helical-vortex rings
• Coherent laminar and turbulent motion of toroidal vortex bundles
• Crow instability in trapped Bose-Einstein condensates
• Reconnections of quantized vortex rings in superfluid ${}^4$He at very low temperatures
• Anomalous vortex ring velocities induced by thermally-excited Kelvin waves and counterflow effects in superfluids
• Topological transition from superuid vortex rings to isolated knots and links
• Interactions between unidirectional quantized vortex rings
• Collective oscillations of a Bose-Einstein condensate induced by a vortex ring
• Three-dimensional stability of leapfrogging quantum vortex rings
• Statistics of vortex loops emitted from quantum turbulence driven by an oscillating sphere
• Theory of Multidimensional Solitons
• Kelvin waves, mutual friction, and fluctuations in the Gross-Pitaevskii model
• Dynamical signature of vortex mass in Fermi superfluids