Abstract
I present a nonlinear differential equation model (DAM) for the spectrum of Kelvin waves on a thin vortex filament. This model preserves the original scaling of the six-wave kinetic equation, its direct and inverse cascade solutions, as well as the thermodynamic equilibrium spectra. Further, I extend DAM to include the effect of sound radiation by Kelvin waves. I show that, because of the phonon radiation, the turbulence spectrum ends at a maximum frequency of ω* ∼ (ε3 c 20s /κ16)1/13, where ε is the total energy injection rate, c s is the speed of sound, and κ is the quantum of circulation.
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Nazarenko, S. Differential approximation for Kelvin wave turbulence. Jetp Lett. 83, 198–200 (2006). https://doi.org/10.1134/S0021364006050031
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DOI: https://doi.org/10.1134/S0021364006050031