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

TL;DR

This paper applies Onsager's ideal turbulence theory to analyze quantum turbulence in the Gross-Pitaevskii model, revealing a double-cascade scenario with distinct behaviors at different scales.

Contribution

It introduces a theoretical framework for quantum turbulence, identifying a quantum stress cascade and its relation to Kelvin-wave cascade, expanding understanding of turbulence at quantum scales.

Findings

Confirmed scale-independence of kinetic energy flux.

Established a double-cascade scenario in quantum turbulence.

Derived the velocity power spectrum using phenomenological arguments.

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.