Title: A new density variance - Mach number relation for subsonic and supersonic, isothermal turbulence Show Chinese title

Title: 一种亚音速和超音速等温湍流的新密度方差-马赫数关系

Abstract: The probability density function (PDF) of the gas density in subsonic and supersonic, isothermal, driven turbulence is analyzed with a systematic set of hydrodynamical grid simulations with resolutions up to 1024^3 cells. We performed a series of numerical experiments with root mean square (r.m.s.) Mach number M ranging from the nearly incompressible, subsonic (M=0.1) to the highly compressible, supersonic (M=15) regime. We study the influence of two extreme cases for the driving mechanism by applying a purely solenoidal (divergence-free) and a purely compressive (curl-free) forcing field to drive the turbulence. We find that our measurements fit the linear relation between the r.m.s. Mach number and the standard deviation of the density distribution in a wide range of Mach numbers, where the proportionality constant depends on the type of the forcing. In addition, we propose a new linear relation between the standard deviation of the density distribution and the standard deviation of the velocity in compressible modes, i.e. the compressible component of the r.m.s. Mach number. In this relation the influence of the forcing is significantly reduced, suggesting a linear relation between the standard deviation of the density distribution and the standard deviation of the velocity in compressible modes, independent of the forcing, ranging from the subsonic to the supersonic regime. Show Chinese abstract

Abstract: 气体密度在亚音速和超音速等温驱动湍流中的概率密度函数（PDF）通过一组系统性的流体动力学网格模拟进行分析，其分辨率高达1024^3个单元。 我们进行了一系列数值实验，其中均方根（r.m.s.）马赫数M从接近不可压缩的亚音速（M=0.1）到高度可压缩的超音速（M=15）范围。 我们通过应用纯涡旋（散度为零）和纯压缩（旋度为零）的强迫场来研究驱动机制的两种极端情况对湍流的影响。 我们发现，在广泛的马赫数范围内，测量结果与均方根马赫数和密度分布的标准偏差之间的线性关系相吻合，其中比例常数取决于强迫类型。 此外，我们提出了一种新的密度分布标准偏差与可压缩模式中速度标准偏差之间的线性关系，即均方根马赫数的可压缩成分。 在这个关系中，强迫的影响显著减少，表明密度分布标准偏差与可压缩模式中速度标准偏差之间存在线性关系，而与强迫无关，从亚音速到超音速范围都适用。