Low Temperature Physics: 36, 785 (2010); https://doi.org/10.1063/1.3499242 (7 pages)
Физика Низких Температур: Том 36, Выпуск 8-9 (Август 2010), c. 986-993    ( к оглавлению , назад )

Weak turbulence of Kelvin waves in superfluid He

Victor S. L’vov1,3 and Sergey Nazarenko2

1Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel

2Mathematics Institute, Warwick University, Coventry, CV4 7AL, UK

3Theoretical Department, Institute for Magnetism, National Academy of Sciences of Ukraine, Kiev, Ukraine
E-mail: victor.lvov@weizmann.ac.il

Received January 21, 2010


Physics of small-scale quantum turbulence in superfluids is essentially based on the knowledge of the energy spectrum of Kelvin waves, Ek. In our paper, we derive a new type of kinetic equation for Kelvin waves on quantized vortex filaments with random large-scale curvature which describes a step-by-step energy cascade over scales caused by five-wave interactions. This approach replaces the previously used six-wave theory, which was recently shown to be inconsistent due to nonlocality. Solving the four-wave kinetic equation, we found a new local spectrum with a universal (curvature-independent) exponent, Ek k µ −5/3, which must replace the nonlocal spectrum of the six-wave theory, Ek k µ −7/5, in future theory, e.g., in finding the quantum turbulence decay rate, found by Kosik and Svistunov under wrong assumption of the locality of energy transfer in the sixwave interactions.

PACS: 67.25.dk Vortices and turbulence;
PACS: 47.37.+q Hydrodynamic aspects of superfluidity; quantum fluids;
PACS: 45.10.Hj Perturbation and fractional calculus methods;
PACS: 47.10.Df Hamiltonian formulations.

Ключевые слова: turbulence, superfluid, Kelvin wave.