Direct Energy Cascade in Two-Dimensional Compressible Quantum Turbulence

Understand

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).