摘要
由瑞利-泰勒(RT)不稳定性失稳所诱导的湍流混合对于自然(如超新星)和工程(如惯性约束聚变)问题都至关重要.RT混合宽度h由气泡高度h_(b)∝α_(b)t^(2)和尖钉高度h_(s)∝α_(s)t^(2)组成,是描述混合的最基本量.一方面,在实际问题中,大多数的RT混合均以高密度比R为特征.在高R下,由于α_(s)>α_(b),h_(s)将对h的增长起主导作用.然而,另一方面,在火箭鞘和线性电子马达上开展的著名实验表明,在高R下,α_(s)(或等价的h_(s))呈高分散性,但其原因或机制没有得到合理解释.在本文中,我们认为可能是由于初始扰动形状的不同造成了α_(s)的高分散性.为了验证这一观点,我们仅改变了尖钉侧初始扰动界面的形状,并基于单模和多模初始扰动,分别设计、模拟并比较了三种形式的初始扰动.结果表明,不同于h_(b)(t)的低依赖性,h_(s)(t)的演化强烈依赖于初始扰动的形状.此外,定量分析表明,尖钉速度的演化与尖钉前缘附近的统计涡量呈正相关.该结果表明,初始扰动对α_(s)(或等价的h_(s))的影响是通过涡实现的,涡在这一过程中起到中间作用.
The turbulent mixing induced by Rayleigh-Taylor instability is of fundamental importance for both nature(e.g.,supernova)and engineering(e.g.,inertial confinement fusion).The mixing width h,composed of bubble height h_(b)∝α_(b)t^(2)and spike height h_(s)∝α_(s)t^(2),is the most primary quantity in describing mixing.On the one hand,at high density ratio R of most practical mixing,h_(s)dominates the growth of h sinceα_(s)>α_(b).On the other hand,however,the well-known experiments conducted on the rocket rig and the linear electric motor indicated a highly scatteredα_(s)(or equivalent h_(s))at high R,without clarifying the reason or mechanism.In this paper,we argue that this phenomenon may be caused by the different shapes of initial perturbation.To validate this viewpoint,by only changing the shape of spike-side interface,three forms of initial perturbations are carefully designed,simulated and compared for both single-mode and multi-mode problems.The comparisons show that the evolution of h_(s)(t)indeed greatly depends on the shape of initial perturbations,distinct from the little dependence of h_(b)(t).Moreover,a quantitative analysis reveals that the evolution of spike velocity has a positive relation with that of statistical vorticity nearby the spike fronts.This implies that the influence of initial perturbation onα_(s)(or equivalent h_(s))is actualized through vortex,which plays an intermediate role.
作者
倪玮丹
曾清红
张又升
Weidan Ni;Qinghong Zeng;Yousheng Zhang(Institute of Applied Physics and Computational Mathematics,Beijing 100094,China)
基金
This work was supported by the National Natural Science Foundation of China(Grant Nos.11972093 and 91852207).
