二维可压缩量子Turbulence中的直接能量级联
Direct Energy Cascade in Two-Dimensional Compressible Quantum Turbulence
摘要：
本文采用Gros-Pitaevskii模型对二维量子湍流进行了数值研究。随着初始能量的大尺度积累，产生了具有多个量子涡点的量子湍流。由于该模式不满足涡度拟能守恒，在衰减情况下，观测到了Kolmogorov-Obukhov能谱$E(k) \propto k^{-5/3}$的直接能量级联，这与二维不可压经典湍流有很大不同.能量通量的正值保证了惯性范围内（从大尺度到小尺度）的\emph{direct}能量级联。在大尺度上的能量几乎全部级联到小尺度上后，可压缩动能实现了热力学平衡态，没有量子化涡旋。
英文摘要：
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.
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