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

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Boué, Laurent, Dasgupta, Ratul, Laurie, Jason, L'vov, Victor S., Nazarenko, Sergey and Procaccia, Itamar. (2011) Exact solution for the energy spectrum of Kelvin-wave turbulence in superfluids. Physical Review B (Condensed Matter and Materials Physics), Vol.84 (No.6). 064516. ISSN 1098-0121

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Official URL: http://dx.doi.org/10.1103/PhysRevB.84.064516

Abstract

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.

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Item Type:	Journal Article
Subjects:	Q Science > QC Physics
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Fluid dynamics, Superfluidity
Journal or Publication Title:	Physical Review B (Condensed Matter and Materials Physics)
Publisher:	American Physical Society
ISSN:	1098-0121
Date:	August 2011
Volume:	Vol.84
Number:	No.6
Page Range:	064516
Identification Number:	10.1103/PhysRevB.84.064516
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	U.S.-Israel Binational Scientific Foundation, Minerva Stiftung, France. Agence nationale de la recherche (ANR)
Grant number:	ANR-09-SYSC-014 (ANR)
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URI:	http://wrap.warwick.ac.uk/id/eprint/38449