Exact solution for the energy spectrum of Kelvin-wave turbulence in superfluids


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.

Publication DOI: https://doi.org/10.1103/PhysRevB.84.064516
Divisions: Engineering & Applied Sciences
Full Text Link: http://journals ... sRevB.84.064516
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PURE Output Type: Article
Published Date: 2011-08-23
Submitted Date: 2011-07-14
Authors: Boué, Laurent
Dasgupta, Ratul
Laurie, Jason ( 0000-0002-3621-6052)
L’vov, Victor
Nazarenko, Sergey
Procaccia, Itamar



Version: Accepted Version

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