Center for Mathematics and Computer Science (CWI), Amsterdam 1098 XG, The Netherlands.
CNR-Nanotec-Unità di Cosenza, Ponte P. Bucci, cubo 31C, 87036 Rende, Italy.
Phys Rev Lett. 2018 Mar 23;120(12):125101. doi: 10.1103/PhysRevLett.120.125101.
Plasma turbulence at scales of the order of the ion inertial length is mediated by several mechanisms, including linear wave damping, magnetic reconnection, the formation and dissipation of thin current sheets, and stochastic heating. It is now understood that the presence of localized coherent structures enhances the dissipation channels and the kinetic features of the plasma. However, no formal way of quantifying the relationship between scale-to-scale energy transfer and the presence of spatial structures has been presented so far. In the Letter we quantify such a relationship analyzing the results of a two-dimensional high-resolution Hall magnetohydrodynamic simulation. In particular, we employ the technique of space filtering to derive a spectral energy flux term which defines, in any point of the computational domain, the signed flux of spectral energy across a given wave number. The characterization of coherent structures is performed by means of a traditional two-dimensional wavelet transformation. By studying the correlation between the spectral energy flux and the wavelet amplitude, we demonstrate the strong relationship between scale-to-scale transfer and coherent structures. Furthermore, by conditioning one quantity with respect to the other, we are able for the first time to quantify the inhomogeneity of the turbulence cascade induced by topological structures in the magnetic field. Taking into account the low space-filling factor of coherent structures (i.e., they cover a small portion of space), it emerges that 80% of the spectral energy transfer (both in the direct and inverse cascade directions) is localized in about 50% of space, and 50% of the energy transfer is localized in only 25% of space.
等离子体中的湍流在离子惯性长度量级上的传播是由多种机制介导的，包括线性波阻尼、磁重联、薄电流片的形成和耗散，以及随机加热。现在人们已经认识到，局部相干结构的存在增强了耗散通道和等离子体的动力学特征。然而，到目前为止，还没有一种正式的方法可以量化尺度间能量传递与空间结构存在之间的关系。在这封信中，我们通过分析二维高分辨率 Hall 磁流体动力学模拟的结果来量化这种关系。具体来说，我们采用空间滤波技术来推导出一个谱能通量项，该项在计算域的任何一点定义了给定波数穿过的谱能的有符号通量。相干结构的特征化是通过传统的二维小波变换来实现的。通过研究谱能通量和小波幅度之间的相关性，我们证明了尺度间传递和相干结构之间的强相关性。此外，通过将一个量与另一个量进行条件化，我们首次能够量化由磁场中拓扑结构引起的湍流级联的非均匀性。考虑到相干结构的空间填充因子低（即它们只占据空间的一小部分），80%的谱能传递（无论是在直接还是逆级联方向上）都集中在大约 50%的空间中，而 50%的能量传递仅集中在 25%的空间中。
