The Importance of Nonlocal Terms in Superfluid Turbulence

C. P. Lorenson

Laurent Boué, Ratul Dasgupta, Jason Laurie +3 more

We study the statistical and dynamical behavior of turbulent Kelvin waves propagating on quantized vortices in superfluids and address the controversy concerning the energy spectrum that is associated with these excitations. Finding the correct energy spectrum is important because Kelvin waves play a major role in the dissipation of energy in superfluid turbulence at near-zero temperatures. In this paper, we show analytically that the solution proposed by [L'vov and Nazarenko, JETP Lett. 91, 428 (2010)] enjoys existence, uniqueness, and regularity of the prefactor. Furthermore, we present numerical results of the dynamical equation that describes to leading order the nonlocal regime of the Kelvin-wave dynamics. We compare our findings with the analytical results from the proposed local and nonlocal theories for Kelvin-wave dynamics and show an agreement with the nonlocal predictions. Accordingly, the spectrum proposed by L'vov and Nazarenko should be used in future theories of quantum turbulence. Finally, for weaker wave forcing we observe an intermittent behavior of the wave spectrum with a fluctuating dissipative scale, which we interpreted as a finite-size effect characteristic of mesoscopic wave turbulence.

Michikazu Kobayashi, Makoto Tsubota

We investigated dynamics of superfluid turbulence by the Gross-Pitaevskii equation and its relation to conventional classical turbulence. We introduced the dissipation term which is effective only in the scale smaller than the core size of quantized vortices, and found that the energy spectrum of superfluid turbulence was consistent with the Kolmogorov law which is one of the most important statistical laws of classical turbulence.

Sergey K. Nemirovskii, Vladimir V. Lebedev

P.-E. Roche

Owen Dix, Rena J. Zieve

Simulating superfluid turbulence using the localized induction approximation allows neighboring parallel vortices to proliferate. In many circumstances a turbulent tangle becomes unsustainable, degenerating into a series of parallel, noninteracting vortex lines. Calculating with the fully nonlocal Biot-Savart law prevents this difficulty but also increases computation time. Here we use a truncated Biot-Savart integral to investigate the effects of nonlocality on homogeneous turbulence. We find that including the nonlocal interaction up to roughly the spacing between nearest-neighbor vortex segments prevents the parallel alignment from developing, yielding an accurate model of homogeneous superfluid turbulence with less computation time.