标题： 可压缩流体动力学湍流的密度功率谱 显示英文标题

标题： Density Power Spectrum of Compressible Hydrodynamic Turbulent Flows

摘要： 湍流在天体物理环境中无处不在，理解湍流介质中的密度结构及其统计特性在天体物理学中具有重要意义。 在本文中，我们通过驱动的等温流体动力学湍流的一维和三维模拟，研究了跨音速和超音速湍流的密度功率谱，$P_{\rho}$，其均方根马赫数范围为$1 \la M_{\rm rms} \la 10$。 从一维实验中我们发现，随着均方根马赫数的增加，密度功率谱的斜率逐渐变平。 这是因为密度分布从具有{\it 不连续性}的$P_{\rho} \propto k^{-2}$对于$M_{\rm rms} \sim 1$的轮廓转变为具有{\it 峰值}的$P_{\rho} \propto k^0$对于$M_{\rm rms} \gg 1$的轮廓。 我们还发现同样的趋势延伸到三维；也就是说，随着马赫数的增加，密度功率谱变平。 但具有$M_{\rm rms} \sim 1$的流动的密度功率谱具有柯尔莫哥洛夫斜率。 The flattening is the consequence of the dominant density structures of {\it 纤维丝} and {\it 纸张}. Observations have claimed different slopes of density power spectra for electron density and cold H I gas in the interstellar medium. We argue that while the Kolmogorov spectrum for electron density reflects the {\it 跨音速} turbulence of $M_{\rm rms} \sim 1$ in the warm ionized medium, the shallower spectrum of cold H I gas reflects the {\it 超音速} turbulence of $M_{\rm rms} \sim$ a few in the cold neutral medium. 显示英文摘要

摘要： Turbulent flows are ubiquitous in astrophysical environments, and understanding density structures and their statistics in turbulent media is of great importance in astrophysics. In this paper, we study the density power spectra, $P_{\rho}$, of transonic and supersonic turbulent flows through one and three-dimensional simulations of driven, isothermal hydrodynamic turbulence with root-mean-square Mach number in the range of $1 \la M_{\rm rms} \la 10$. From one-dimensional experiments we find that the slope of the density power spectra becomes gradually shallower as the rms Mach number increases. It is because the density distribution transforms from the profile with {\it discontinuities} having $P_{\rho} \propto k^{-2}$ for $M_{\rm rms} \sim 1$ to the profile with {\it peaks} having $P_{\rho} \propto k^0$ for $M_{\rm rms} \gg 1$. We also find that the same trend is carried to three-dimension; that is, the density power spectrum flattens as the Mach number increases. But the density power spectrum of the flow with $M_{\rm rms} \sim 1$ has the Kolmogorov slope. The flattening is the consequence of the dominant density structures of {\it filaments} and {\it sheets}. Observations have claimed different slopes of density power spectra for electron density and cold H I gas in the interstellar medium. We argue that while the Kolmogorov spectrum for electron density reflects the {\it transonic} turbulence of $M_{\rm rms} \sim 1$ in the warm ionized medium, the shallower spectrum of cold H I gas reflects the {\it supersonic} turbulence of $M_{\rm rms} \sim$ a few in the cold neutral medium.