Tritschler V K, Zubel M, Hickel S, Adams N A
Institute of Aerodynamics and Fluid Mechanics, Technische Universität München, 85747 Garching, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Dec;90(6):063001. doi: 10.1103/PhysRevE.90.063001. Epub 2014 Dec 1.
In this study we present direct numerical simulation results of the Richtmyer-Meshkov instability (RMI) initiated by Ma=1.05,Ma=1.2, and Ma=1.5 shock waves interacting with a perturbed planar interface between air and SF(6). At the lowest shock Mach number the fluids slowly mix due to viscous diffusion, whereas at the highest shock Mach number the mixing zone becomes turbulent. When a minimum critical Taylor microscale Reynolds number is exceeded, an inertial range spectrum emerges, providing further evidence of transition to turbulence. The scales of turbulent motion, i.e., the Kolmogorov length scale, the Taylor microscale, and the integral length, scale are presented. The separation of these scales is found to increase as the Reynolds number is increased. Turbulence statistics, i.e., the probability density functions of the velocity and its longitudinal and transverse derivatives, show a self-similar decay and thus that turbulence evolving from RMI is not fundamentally different from isotropic turbulence, though nominally being only isotropic and homogeneous in the transverse directions.
在本研究中，我们给出了马赫数Ma = 1.05、Ma = 1.2和Ma = 1.5的激波与空气和SF(6)之间的扰动平面界面相互作用引发的里希特迈尔-梅什科夫不稳定性（RMI）的直接数值模拟结果。在最低激波马赫数下，由于粘性扩散，流体缓慢混合，而在最高激波马赫数下，混合区变为湍流。当超过最小临界泰勒微尺度雷诺数时，出现惯性范围谱，这为向湍流过渡提供了进一步的证据。给出了湍流运动的尺度，即科尔莫戈罗夫长度尺度、泰勒微尺度和积分长度尺度。发现随着雷诺数的增加，这些尺度的分离增大。湍流统计量，即速度及其纵向和横向导数的概率密度函数，呈现出自相似衰减，因此由RMI演化而来的湍流与各向同性湍流在本质上没有差异，尽管名义上仅在横向是各向同性和均匀的。
