Differential approximation for Kelvin-wave turbulence

Details Differential approximation for Kelvin-wave turbulence Differential approximation for Kelvin-wave turbulence

2005-11-05

arxiv.org/abs/cond-mat/0511136v3

Physics

Condensed Matter

Statistical Mechanics

Prepared of publication in JETP Letters

Scientific paper

10.1134/S0021364006050031

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 $\omega^* \sim (\epsilon^3 c_s^{20} / \kappa^{16})^{1/13}$ where $\epsilon$ is the total energy injection rate, $c_s$ is the speed of sound and $\kappa$ is the quantum of circulation.

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