Weak turbulence of Kelvin waves in superfluid He

Анотація

Physics of small-scale quantum turbulence in superfluids is essentially based on the knowledge of the energy spectrum of Kelvin waves, E_k. 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, E_k k µ ^−5/3, which must replace the nonlocal spectrum of the six-wave theory, E_k 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.