Interaction of Kelvin waves and nonlocality of energy transfer in superfluids
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.
 Publication:

Physical Review B
 Pub Date:
 March 2010
 DOI:
 10.1103/PhysRevB.81.104526
 arXiv:
 arXiv:0911.1733
 Bibcode:
 2010PhRvB..81j4526L
 Keywords:

 67.25.dk;
 47.37.+q;
 45.10.Hj;
 47.10.Df;
 Vortices and turbulence;
 Hydrodynamic aspects of superfluidity;
 quantum fluids;
 Perturbation and fractional calculus methods;
 Hamiltonian formulations;
 Nonlinear Sciences  Chaotic Dynamics;
 Condensed Matter  Superconductivity;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 Physics  Fluid Dynamics
 EPrint:
 16 pages, resubmitted to PRB on 14 February, 2010