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arXiv:1006.4315 · Physical Review B

Anomalous vortex-ring velocities induced by thermally excited Kelvin waves and counterflow effects in superfluids

Giorgio Krstulovic, Marc Brächet

Published Apr 21, 2011• 20 citations
arXivHTMLPDF

Abstract

Dynamical counterflow effects on vortex evolution under the truncated Gross-Pitaevskii equation are investigated. Standard longitudinal mutual-friction effects are produced and a dilatation of vortex rings is obtained at large counterflows. A strong temperature-dependent anomalous slowdown of vortex rings is observed and attributed to the presence of thermally excited Kelvin waves. This generic effect of finite-temperature superfluids is estimated using energy equipartition and orders of magnitude are given for weakly interacting Bose-Einstein condensates and superfluid $^{4}\mathrm{He}$. The relevance of thermally excited Kelvin waves is discussed in the context of quantum turbulence.

DOI
10.1103/physrevb.83.132506

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Dynamical counterflow effects on vortex evolution under the truncated Gross-Pitaevskii equation are investigated. Standard longitudinal mutual-friction effects are produced and a dilatation of vortex rings is obtained at large counterflows. A strong temperature-dependent anomalous slowdown of vortex rings is observed and attributed to the presence of thermally excited Kelvin waves. This generic effect of finite-temperature superfluids is estimated using energy equipartition and orders of magnitude are given for weakly interacting Bose-Einstein condensates and superfluid 4He^{4}\mathrm{He}4He. The relevance of thermally excited Kelvin waves is discussed in the context of quantum turbulence.
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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.
We explore instabilities in binary superfluids with a nonvanishing relative superflow, particularly focusing on counterflow and coflow instabilities. We extend recent results on the thermodynamic origin of finite superflow instabilities in single-component superfluids to binary systems and derive a criterion for the onset of instability through a hydrodynamic analysis, which applies to interacting many-body systems at finite temperature. We find that the onset of these instabilities is signaled by the determinant of the Hessian of the thermal free energy diverging and changing sign. We verify this hydrodynamic prediction in a holographic binary superfluid modeled with gauge/gravity duality, which naturally incorporates strong coupling, finite temperature, and dissipation. We also compare to results obtained using the Gross-Pitaevskii equation for weakly interacting Bose-Einstein condensates and find that the same criterion continues to apply at zero temperature, where it reduces to evaluating derivatives of the supercurrents with respect to the superfluid velocities. We observe that the critical velocities of these instabilities follow a general scaling law related to the interaction strength between superfluid components. Finally, the nonlinear stages of the instabilities are studied by full time evolution using gauge/gravity duality, where vortex annihilation leads to a decrease of superfluid velocity back to a value where the binary superfluid phase is stable.