可压缩磁流体动力学流中的平均场和涨落
Mean fields and fluctuations in compressible magnetohydrodynamic flows
摘要：
我们应用高斯平滑，以获得平均磁场，密度，速度，和磁场和动能密度从我们的数值模型的星际介质，基于三维磁流体动力学方程在剪切盒$1 \times 1 \times 2 \, {\rm kpc}$的大小。星际介质是高度可压缩的，因为湍流是跨音速或超音速的;因此，这是一个很好的背景下，探索使用平滑来表示物理变量在可压缩介质中的平均和波动部分。与水平平均等替代平均过程不同，高斯平滑保留了平均场的三维结构。虽然高斯平滑不遵守雷诺平均规则，但Germano（1992）建议定义了物理上有意义且数学上合理的中心统计矩。我们讨论的方法来确定一个最佳的平滑尺度$\ell$和这种选择的结果的影响。通过对磁场、密度场和速度场的谱分析，我们找到了一个适合于这三个场的平滑长度，即$\ell \approx 75 \, {\rm pc}$。这样的平滑尺度可能对模拟参数的选择敏感;这可能会在未来的工作中考虑，但这里我们只是探讨方法。本文讨论了可压缩流中动能密度涨落的三阶统计矩的性质，并给出了它们的物理解释。平均磁场被平均场发电机放大，显著改变了空间和尺度之间的动能分布，降低了中间尺度的动能大小。这种中等尺度的动能是一个有用的诊断SN驱动外流的重要性。
英文摘要：
We apply Gaussian smoothing to obtain mean magnetic field, density, velocity, and magnetic and kinetic energy densities from our numerical model of the interstellar medium, based on three-dimensional magnetohydrodynamic equations in a shearing box $1 \times 1 \times 2 \, {\rm kpc}$ in size. The interstellar medium is highly compressible, as the turbulence is transonic or supersonic; it is thus an excellent context in which to explore the use of smoothing to represent physical variables in a compressible medium in terms of their mean and fluctuating parts. Unlike alternative averaging procedures, such as horizontal averaging, Gaussian smoothing retains the three-dimensional structure of the mean fields. Although Gaussian smoothing does not obey the Reynolds rules of averaging, physically meaningful and mathematically sound central statistical moments are defined as suggested by Germano (1992). We discuss methods to identify an optimal smoothing scale $\ell$ and the effects of this choice on the results. From spectral analysis of the magnetic, density and velocity fields, we find a suitable smoothing length for all three fields, of $\ell \approx 75 \, {\rm pc}$. Such a smoothing scale is likely to be sensitive to the choice of simulation parameters; this may be considered in future work, but here we just explore the methodology. We discuss the properties of third-order statistical moments in fluctuations of kinetic energy density in compressible flows, and suggest their physical interpretation. The mean magnetic field, amplified by a mean-field dynamo, significantly alters the distribution of kinetic energy in space and between scales, reducing the magnitude of kinetic energy at intermediate scales. This intermediate-scale kinetic energy is a useful diagnostic of the importance of SN-driven outflows.
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