Differential approximation for Kelvin-wave turbulence

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

Prepared of publication in JETP Letters

References in corpus (4)

• Kelvin Wave Cascade and Decay of Superfluid Turbulence
• A Kelvin-wave cascade on a vortex in superfluid ${}^4$He at a very low temperature
• Scale Separation Scheme for Simulating Superfluid Turbulence: Kelvin-Wave Cascade
• Energy spectra of developed superfluid turbulence

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• Quantum turbulence in trapped atomic Bose-Einstein condensates
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• Energy Spectra of Developed Turbulencein Helium Superfluids
• Quantum turbulence in quantum gases
• Modeling Kelvin Wave Cascades in Superfluid Helium
• Sustained turbulence in the three-dimensional Gross-Pitaevskii model
• Scanning Superfluid-Turbulence Cascade by Its Low-Temperature Cutoff
• Kelvin-wave turbulence generated by vortex reconnections
• Wave turbulence in self-gravitating Bose gases and nonlocal nonlinear optics
• Nonlinear Diffusion Models for Gravitational Wave Turbulence
• Direct Evidence of a Dual Cascade in Gravitational Wave Turbulence
• Kelvin waves and the decay of quantum superfluid turbulence
• Momentum distribution of Vinen turbulence in trapped atomic Bose-Einstein condensates
• Inverse cascade anomalies in fourth-order Leith models
• Mixed flux-equipartition solutions of a diffusion model of nonlinear cascades