三维k空间约化功率谱的正演模拟
Forward Modeling of Reduced Power Spectra From Three-Dimensional k-Space
摘要：
我们提出了一个数值正演模型的结果，以评估一维约化功率谱密度（PSD）从任意的能量分布在$\mathbf{k}$空间。在这个模型中，我们可以单独计算不可压轴对称湍流的谱张量的对角元素。给出了一个临界平衡的湍流叶栅与$k_\|\sim k_\perp^α$和$α<1$，我们探讨了作为频率的函数的约化PSD的含义。光谱是在泰勒假设下得到的。我们进一步研究了光谱指数$κ$对等离子体流和背景磁场之间的场-流角$θ$的函数依赖性。我们表明，临界平衡湍流渐近发展的$θ$ -独立的光谱与斜率对应的垂直级联。这发生在过渡频率$f_{2D}(L,α,θ)$处，该过渡频率是分析估计的并且取决于外尺度$L$、临界平衡指数$α$和场-流角$θ$。讨论了各向异性阻尼项对$\mathbf{k}$能量空间分布的影响及其对PSD的影响。此外，我们还证明了Horbury等人（2008）和Chen等人（2010）在太阳风中发现的光谱各向异性$κ(θ)$与动力学Alfvén波的阻尼临界平衡级联一致。我们还对von Papen等人（2014）在土星等离子体片中获得的功率谱进行了建模，发现$9\,R_\mathrm{s}$内部光谱指数的变化可以通过电子尺度上的阻尼来解释。
英文摘要：
We present results from a numerical forward model to evaluate one-dimensional reduced power spectral densities (PSD) from arbitrary energy distributions in $\mathbf{k}$-space. In this model, we can separately calculate the diagonal elements of the spectral tensor for incompressible axisymmetric turbulence with vanishing helicity. Given a critically balanced turbulent cascade with $k_\|\sim k_\perp^α$ and $α<1$, we explore the implications on the reduced PSD as a function of frequency. The spectra are obtained under the assumption of Taylor's hypothesis. We further investigate the functional dependence of the spectral index $κ$ on the field-to-flow angle $θ$ between plasma flow and background magnetic field from MHD to electron kinetic scales. We show that critically balanced turbulence asymptotically develops toward $θ$-independent spectra with a slope corresponding to the perpendicular cascade. This occurs at a transition frequency $f_{2D}(L,α,θ)$, which is analytically estimated and depends on outer scale $L$, critical balance exponent $α$ and field-to-flow angle $θ$. We discuss anisotropic damping terms acting on the $\mathbf{k}$-space distribution of energy and their effects on the PSD. Further, we show that the spectral anisotropies $κ(θ)$ as found by Horbury et al. (2008) and Chen et al. (2010) in the solar wind are in accordance with a damped critically balanced cascade of kinetic Alfvén waves. We also model power spectra obtained by von Papen et al. (2014) in Saturn's plasma sheet and find that the change of spectral indices inside $9\,R_\mathrm{s}$ can be explained by damping on electron scales.
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