Direct energy cascade in two-dimensional compressible quantum turbulence

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) ∝ 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 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.

Numerical Studies of Quantum Turbulence

“…Recently, 2D turbulence in the GP model has been actively studied, and the 2D nature has been found [138,139,140,141,142,143,144,145,146,147,148,149]. For example, the dynamical clustering of quantized vortices, namely, Onsager vortex formation, has been numerically confirmed [146,148], which is consistent with behavior of the energy inverse cascade in 2D classical turbulence.…”

“…The result of Ref. [139] has already been reviewed in Ref. [4]; in this subsection, we describe the other study showing the evidence of the inverse cascade in QT [144].…”

“…Thus, it seems that the inverse cascade in QT may not occur. In fact, Numasato et al have argued for the non-existence of the inverse cascade [139]. However, some studies obtain evidence of the inverse cascade in QT [138,144].…”

“…There are many studies for 2D QT [129,130,138,139,140,141,142,143,144,145,146,147,148,149], some of which discuss the possibility of the inverse cascade in QT. To our understanding, the existence of the inverse cascade in QT is controversial.…”

Relaxation of superfluid turbulence in highly oblate Bose-Einstein condensates

“…An interesting question is whether the inverse cascade can occur in an atomic BEC. Since the enstrophy, proportional to the total number of quantized vortices in quantum turbulence, is not conserved in a compressible 2D superfluid due to the vortex-antivortex annihilation, there has been a theoretical controversy on this issue [11][12][13][14][15][16][17][18][19][20]. Recently, Neely et al [21] reported an experimental and numerical study to show that there are conditions for which 2D turbulence in a BEC can dissipatively evolve into large-scale flow.…”