Department of Physics, University of Oslo, P.O. 1048 Blindern, 0316 Oslo, Norway.
Phys Rev E. 2017 May;95(5-1):052144. doi: 10.1103/PhysRevE.95.052144. Epub 2017 May 30.
We establish a statistical relationship between the inverse energy cascade and the spatial correlations of clustered vortices in two-dimensional quantum turbulence. The Kolmogorov spectrum k^{-5/3} on inertial scales r corresponds to a pair correlation function between the vortices with different signs that decays as a power law with the pair distance given as r^{-4/3}. To test these scaling relations, we propose a forced and dissipative point vortex model that captures the turbulent dynamics of quantized vortices by the emergent clustering of same-sign vortices. The inverse energy cascade developing in a statistically neutral system originates from this vortex clustering that evolves with time.
我们建立了逆能级联与二维量子湍流中聚集涡旋的空间相关性之间的统计关系。惯性尺度 r 上的 Kolmogorov 谱 k^{-5/3}对应于具有不同符号的涡旋之间的对关联函数，该函数随着对距离 r^{-4/3}的幂律衰减。为了检验这些标度关系，我们提出了一个受迫耗散点涡模型，该模型通过相同符号涡旋的突发聚类来捕捉量子涡旋的湍流动力学。在统计上中性系统中发展的逆能级联源于这种随时间演化的涡旋聚类。
