Direct Energy Cascade in Two-Dimensional Compressible Quantum Turbulence

TL;DR

This study numerically demonstrates a direct energy cascade in two-dimensional compressible quantum turbulence, characterized by a Kolmogorov spectrum, differing from classical turbulence due to lack of enstrophy conservation.

Contribution

It reveals the occurrence of a direct energy cascade with a Kolmogorov spectrum in 2D compressible quantum turbulence, a phenomenon not observed in classical 2D turbulence.

Findings

Observation of a Kolmogorov--Obukhov energy spectrum $E(k) \,\propto\, k^{-5/3}$

Confirmation of a positive energy flux indicating a direct cascade

Energy transfer leads to thermodynamic equilibrium at small scales

Abstract

We numerically study two-dimensional quantum turbulence with a Gross--Pitaevskii model. With the energy initially accumulated at large scale, quantum turbulence with many quantized vortex points is generated. Due to the lack of enstrophy conservation in this model, direct energy cascade with a Kolmogorov--Obukhov energy spectrum $E(k) \propto k^{-5/3}$ is observed, which is quite different from two-dimensional incompressible classical turbulence in the decaying case. A positive value for the energy flux guarantees a \emph{direct} energy cascade in the inertial range (from large to small scales). After almost all the energy at the large scale cascades to the small scale, the compressible kinetic energy realizes the thermodynamic equilibrium state without quantized vortices.