Theoretical analysis of quantum turbulence using the Onsager "ideal turbulence" theory

Abstract

We investigate three-dimensional quantum turbulence as described by the Gross-Pitaevskii model using the analytical method exploited in the Onsager "ideal turbulence" theory. We derive the scale-independence of the scale-to-scale kinetic energy flux and establish a double-cascade scenario: at scales much larger than the mean intervortex ${\ell }_i$, the Richardson cascade becomes dominant, whereas at scales much smaller than ${\ell }_i$, another type of cascade is induced by quantum stress. We then evaluate the corresponding velocity power spectrum using a phenomenological argument. The relation between the novel cascade, which we call quantum stress cascade, and the Kelvin-wave cascade is also discussed.

20 pages, 2 figures. Minor revisions are made in ver. 3

References in corpus (13)

• Introduction to quantum turbulence
• Dynamic Alignment in Driven Magnetohydrodynamic Turbulence
• Bottleneck crossover between classical and quantum superfluid turbulence
• Quantum Turbulence in a Trapped Bose-Einstein Condensate
• Energy spectra of vortex distributions in two-dimensional quantum turbulence
• Turbulent velocity spectra in superfluid flows
• Quantum Turbulence
• Gradual eddy-wave crossover in superfluid turbulence
• Dual cascade and dissipation mechanisms in helical quantum turbulence
• Intermittency of quantum turbulence with superfluid fractions from 0% to 96%
• Baropycnal Work: A Mechanism for Energy Transfer Across Scales
• The Decay of Pure Quantum Turbulence in Superfluid 3He-B
• Scale locality and the inertial range in compressible turbulence

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