Weak turbulence of Kelvin waves in superfluid He

Abstract

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⁻⁵/³, which must replace the nonlocal spectrum of the six-wave theory, Ek∝k⁻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.