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arXiv:cond-mat/0205588

Decay of superfluid turbulence via Kelvin wave radiation and vortex reconnections

M. L. Leadbeater, David C. Samuels, Carlo F. Barenghi, Charles S. Adams

Published May 28, 2002• 0 citations
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Abstract

The elementary processes involved in the decay of superfluid turbulence in the limit of low temperature are studied by numerical simulations of vortex ring collisions. We find that small vortex rings produced by reconnections eventually annihilate in a collision where all their energy is converted into Kelvin waves and sound. We show that sound emission due to Kelvin waves also leads to a loss of vortex line length but this dissipation mechanism alone is too small to account for the experimentally observed decay.

DOI
10.48550/arxiv.cond-mat/0205588

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The elementary processes involved in the decay of superfluid turbulence in the limit of low temperature are studied by numerical simulations of vortex ring collisions. We find that small vortex rings produced by reconnections eventually annihilate in a collision where all their energy is converted into Kelvin waves and sound. We show that sound emission due to Kelvin waves also leads to a loss of vortex line length but this dissipation mechanism alone is too small to account for the experimentally observed decay.
The decay of superfluid turbulence in the limit of low temperature is studied by numerical simulations of vortex ring collisions. In particular we excite Kelvin waves and study the loss of vortex line length due to Kelvin-wave radiation. Although the effect is small, the decay constant is not inconsistent with recent experiments on vortex lattices in dilute Bose-Einstein condensates, and on superfluid turbulence in helium at very low temperature. We also consider the character of the decay when both vortex reconnections and Kelvin-wave radiation are present.
There are several ways to create the vorticity-free solitary waves --- rarefaction pulses --- in condensates: by the process of strongly nonequilibrium condensate formation in a weakly interacting Bose gas, by creating local depletion of the condensate density by a laser beam, and by moving a small object with supercritical velocities. Perturbations created by such waves colliding with vortices are studied in the context of the Gross-Pitaevskii model. We find that the effect of the interactions consists of two competing mechanisms: the creation of vortex line as rarefaction waves acquire circulation in a vicinity of a vortex core and the loss of the vortex line to sound due to Kelvin waves that are generated on vortex lines by rarefaction pulses. When a vortex ring collides with a rarefaction wave, the ring either stabilizes to a smaller ring after emitting sound through Kelvin-wave radiation or the entire energy of the vortex ring is lost to sound if the radius of the ring is of the order of the healing length. We show that during the time evolution of a tangle of vortices, the interactions with rarefaction pulses provide an important dissipation mechanism enhancing the decay of superfluid turbulence.
We study numerically the interaction of four initial superfluid vortex rings in the absence of any dissipation or friction. We find evidence for a cascade of Kelvin waves generated by individual vortex reconnection events which transfers energy to higher and higher wave numbers k. After the vortex reconnections occur, the energy spectrum scales as k(-1) and the curvature spectrum becomes flat. These effects highlight the importance of Kelvin waves and reconnections in the transfer of energy within a turbulent vortex tangle.
Kelvin waves---helical waves on quantized vortex lines---are the normal modes of vortices in a superfluid. At zero temperature, the only dissipative channel of vortex dynamics is phonon emission. Starting with the hydrodynamic action, we derive the Hamiltonian of vortex-phonon interaction, thereby reducing the problem of the interaction of Kelvin waves with sound to inelastic elementary excitation scattering. On the basis of this formalism, we calculate the rate of sound radiation by superfluid turbulence at zero temperature and estimate the value of short-wavelength cutoff of the turbulence spectrum.
We investigate quantum vortex ring dynamics at scales smaller than the inter-vortex spacing in quantum turbulence. Through geometrical arguments and high-resolution numerical simulations, we examine the validity of simple estimates for the mean free path and the structure of vortex rings post-reconnection. We find that a large proportion of vortex rings remain coherent objects where approximately 75% of their energy is preserved. This leads us to consider the effectiveness of energy transport in turbulent tangles. Moreover, we show that in low density tangles, appropriate for the ultra-quantum regime, ring emission cannot be ruled out as an important mechanism for energy dissipation. However at higher vortex line densities, typically associated with the quasi-classical regime, loop emission is expected to make a negligible contribution to energy dissipation, even allowing for the fact that our work shows rings can survive multiple reconnection events. Hence the Kelvin wave cascade seems the most plausible mechanism leading to energy dissipation.
By performing numerical simulations based on the Gross-Pitaevskii equation, we make direct quantitative measurements of the sound energy released due to superfluid vortex reconnections. We show that the energy radiated expressed in terms of the loss of vortex line length is a simple function of the reconnection angle. In addition, we study the temporal and spatial distribution of the radiation and show that energy is emitted in the form of a sound pulse with a wavelength of a few healing lengths.