Abstract
We derive a type of kinetic equation for Kelvin waves on quantized vortex filaments with random large-scale curvature, that describes step-by-step (local) energy cascade over scales caused by 4-wave interactions. Resulting new energy spectrum E LN(k) ∝ k −5/3 must replace in future theory (e.g., in finding the quantum turbulence decay rate) the previously used spectrum E KS(k) ∝ k −7/5, which was recently shown to be inconsistent due to nonlocality of the 6-wave energy cascade.
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L’vov, V.S., Nazarenko, S. Spectrum of Kelvin-wave turbulence in superfluids. Jetp Lett. 91, 428–434 (2010). https://doi.org/10.1134/S002136401008014X
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DOI: https://doi.org/10.1134/S002136401008014X