论文标题
初始扰动功率光谱对Richtmyer-Meshkov不稳定性引起的湍流混合层的生长的影响
The influence of initial perturbation power spectra on the growth of a turbulent mixing layer induced by Richtmyer-Meshkov instability
论文作者
论文摘要
本文研究了不同的宽带扰动对Richtmyer的演变的影响 - 由Mach 1.84冲击启动的Richtmyer-Meshkov湍流混合层，横穿扰动界面，其密度比为3：1的扰动界面。界面扰动中模式的带宽及其相对振幅都在一系列精心设计的数值模拟中变化，在网格分辨率下，最高$ 3.2 \ times10^9 $单元。考虑了三种不同的扰动，其特征是$ p（k）\ propto k^m $的功率谱，其中$ m = -1 $，$ -2 $和$ -3 $。混合层的增长显示在很大程度上取决于初始条件，其增长率指数$θ$的每个值为$ 0.5 $，0.63美元和$ 0.75 $，每个值在最高网格分辨率下为$ m $。分子混合分数$θ$的渐近值也显示出$ m $的差异；在最近的时间，认为$θ$分别为$ 0.56 $，$ 0.39 $和$ 0.20 $。还分析了在时间和光谱域中的湍流动能（TKE）。发现TKE的时间衰减率不匹配$ n =2-3θ$的预测值，这证明是由于时间变化{归一化的耗散率$C_ε$}。在频谱空间中，数据遵循低波数的理论上缩放$ k^{（m+2）/2} $，趋向于$ k^{ - 3/2} $和$ k^{ - 5/3} $缩放，分别是横向和正常速度组件的光谱的缩放。结果代表了先前关于Richtmyer的工作的显着扩展，即从宽带初始扰动演变而来，并为将来的研究提供了有用的基准。
This paper investigates the influence of different broadband perturbations on the evolution of a Richtmyer--Meshkov turbulent mixing layer initiated by a Mach 1.84 shock traversing a perturbed interface separating gases with a density ratio of 3:1. Both the bandwidth of modes in the interface perturbation, as well as their relative amplitudes, are varied in a series of carefully designed numerical simulations at grid resolutions up to $3.2\times10^9$ cells. Three different perturbations are considered, characterised by a power spectrum of the form $P(k)\propto k^m$ where $m=-1$, $-2$ and $-3$. The growth of the mixing layer is shown to strongly depend on the initial conditions, with the growth rate exponent $θ$ found to be $0.5$, $0.63$ and $0.75$ for each value of $m$ at the highest grid resolution. The asymptotic values of the molecular mixing fraction $Θ$ are also shown to vary significantly with $m$; at the latest time considered $Θ$ is $0.56$, $0.39$ and $0.20$ respectively. Turbulent kinetic energy (TKE) is also analysed in both the temporal and spectral domains. The temporal decay rate of TKE is found not to match the predicted value of $n=2-3θ$, which is shown to be due to a time-varying {normalised dissipation rate $C_ε$}. In spectral space, the data follow the theoretical scaling of $k^{(m+2)/2}$ at low wavenumbers and tend towards $k^{-3/2}$ and $k^{-5/3}$ scalings at high wavenumbers for the spectra of transverse and normal velocity components respectively. The results represent a significant extension of previous work on the Richtmyer--Meshkov instability evolving from broadband initial perturbations and provide useful benchmarks for future research.
