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Interaction of Kelvin waves and nonlocality of energy transfer in superfluids
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Laurie, Jason, L'vov, V. S., Nazarenko, Sergey and Rudenko, Oleksii. (2010) Interaction of Kelvin waves and nonlocality of energy transfer in superfluids. Physical Review B (Condensed Matter and Materials Physics), Vol.81 (No.10). ISSN 10980121

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Official URL: http://dx.doi.org/10.1103/PhysRevB.81.104526
Abstract
We argue that the physics of interacting Kelvin Waves (KWs) is highly nontrivial and cannot be understood on the basis of pure dimensional reasoning. A consistent theory of KW turbulence in superfluids should be based upon explicit knowledge of their interactions. To achieve this, we present a detailed calculation and comprehensive analysis of the interaction coefficients for KW turbuelence, thereby, resolving previous mistakes stemming from unaccounted contributions. As a first application of this analysis, we derive a local nonlinear (partial differential) equation. This equation is much simpler for analysis and numerical simulations of KWs than the BiotSavart equation, and in contrast to the completely integrable local induction approximation (in which the energy exchange between KWs is absent), describes the nonlinear dynamics of KWs. Second, we show that the previously suggested KozikSvistunov energy spectrum for KWs, which has often been used in the analysis of experimental and numerical data in superfluid turbulence, is irrelevant, because it is based upon an erroneous assumption of the locality of the energy transfer through scales. Moreover, we demonstrate the weak nonlocality of the inverse cascade spectrum with a constant particlenumber flux and find resulting logarithmic corrections to this spectrum.
Item Type:  Journal Article  

Subjects:  Q Science > QC Physics  
Divisions:  Faculty of Science > Mathematics  
Library of Congress Subject Headings (LCSH):  Waves, Superfluidity, Turbulence  
Journal or Publication Title:  Physical Review B (Condensed Matter and Materials Physics)  
Publisher:  American Physical Society  
ISSN:  10980121  
Official Date:  26 March 2010  
Dates: 


Volume:  Vol.81  
Number:  No.10  
Number of Pages:  14  
Identification Number:  10.1103/PhysRevB.81.104526  
Status:  Peer Reviewed  
Access rights to Published version:  Open Access  
References:  [1] E. Kozik and B. Svistunov, Phys. Rev. Lett. 92, 035301 

URI:  http://wrap.warwick.ac.uk/id/eprint/3959 
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