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arXiv 0705.2464astro-ph
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可压缩MHD Turbulence的标度关系

Scaling Relations of Compressible MHD Turbulence

Grzegorz Kowal, A. Lazarian

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4 pages, 5 figures
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摘要：

研究了可压缩强磁化湍流的标度关系。我们发现我们的结果与Fleck（1996）可压缩流体动力学湍流模型有很好的一致性。特别是，我们发现Kritsuk等人（2007）提出的密度加权速度，即$u \equiv ρ^{1/3} v$，服从Kolmogorov标度，即高马赫数湍流的$E_{u}(k)\sim k^{-5/3}$。同样，我们发现对于所研究的所有马赫数，$u$的三阶结构函数的指数都保持等于1。高阶关联的标度性服从She-Leveque（1994）的二维耗散结构标度性，且不随马赫数变化。与$v$相比，$v$在平行和垂直于局部磁场的方向上表现出不同的缩放，$u$的缩放在两个方向上是相似的。此外，我们发现，密度的峰值产生了一个层次，其中物理和列密度都随着规模的减少，根据弗莱克（1996年）的预测。这种层次结构可以与星际气体中普遍存在的小的电离和中性结构（ESTs）联系起来。我们认为，研究的统计列密度峰值可以提供一致性检查的湍流速度的研究和洞察超音速湍流，当速度信息是不可用的。

英文摘要：

We study scaling relations of compressible strongly magnetized turbulence. We find a good correspondence of our results with the Fleck (1996) model of compressible hydrodynamic turbulence. In particular, we find that the density-weighted velocity, i.e. $u \equiv ρ^{1/3} v$, proposed in Kritsuk et al. (2007) obeys the Kolmogorov scaling, i.e. $E_{u}(k)\sim k^{-5/3}$ for the high Mach number turbulence. Similarly, we find that the exponents of the third order structure functions for $u$ stay equal to unity for the all the Mach numbers studied. The scaling of higher order correlations obeys the She-Leveque (1994) scalings corresponding to the two-dimensional dissipative structures, and this result does not change with the Mach number either. In contrast to $v$ which exhibits different scaling parallel and perpendicular to the local magnetic field, the scaling of $u$ is similar in both directions. In addition, we find that the peaks of density create a hierarchy in which both physical and column densities decrease with the scale in accordance to the Fleck (1996) predictions. This hierarchy can be related ubiquitous small ionized and neutral structures (SINS) in the interstellar gas. We believe that studies of statistics of the column density peaks can provide both consistency check for the turbulence velocity studies and insight into supersonic turbulence, when the velocity information is not available.

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