Rayleigh-Taylor turbulence: self-similar analysis and direct numerical simulations
Rayleigh-Taylor turbulence: self-similar analysis and direct numerical simulations
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DOI：
10.1017/s0022112004008286
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发表时间：
2004-05-25
影响因子：
3.7
通讯作者：
Clark, TT
中科院分区：
文献类型：
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作者：
Ristorcelli, JR;Clark, TT
(D)采用单流体Boussmesq瑞利-泰勒不稳定性和向湍流过渡的直接数值模拟和自相似分析来研究瑞利-泰勒湍流。施密特、阿特伍德和体积雷诺数Sc = 1。A = 0.01， Re小于或等于3000。采用高雷诺数矩自相似理论，与耗散的能量级联解释相一致，对DNS结果进行了分析。混合层宽度服从解为h（t - C-o）的微分方程，h(0)) = (1)/(4)C(o)Agt(2) + rootAgC(o)h(0)(1/2) t + h(0)；h（t; c - 0, h(0)）的结果是一个严格的结果，只有一个自相似性。它表明了一个中间时间制度，其中增长是线性的和虚拟原点的重要性。长期以来，与(1)/(4)C(o)Agt(2)标度相似的众所周知的h占主导地位。自相似分析表明渐近增长率不具有普适性。得到了二阶矩的标量、它们的耗散和生产耗散比，并与DNS进行了比较。流不是传统意义上的自相似，没有单一的长度尺度来衡量流。矩相似法产生了三种不同的湍流含能长度尺度e、泰勒微尺度lambda和Kolmogorov耗散尺度eta。DNS和自相似分析是一致的，显示l类似于Agt(2)， lambda相似于t（1/2）和etasassimilar于((A(2)g(2)/v(3))t)(-1/4)，在湍流生长阶段开始的三个初始涡流中实现自相似行为，体积雷诺数在Re = 800-1000范围内，取决于初始条件。出现了一幅湍流的图像，其中最大的尺度随着t(2)渐近增长，最小的尺度随着t（-1/4）减小。因此，湍流谱的带宽随t（9/4）增长，符合完全发展的平稳湍流的R-t(3/4) Kolmogorov标度定律。虽然不是所有的矩都是一致的，尤其是边缘区域的耗散和高阶矩，但根据自相似的结果，似乎可以得出这样的结论：(i)湍流长度尺度以h（t; C-o, h(0)）的幂次演变；(n)自相似瑞利-泰勒湍流的数学证明和DNS的数值证明，alpha不是一个普遍常数；（111）减小a与降低初始谱的低波数载荷之间存在统计学上显著的相关性。
(D)irect numerical simulations and a self-similar analysis of the single-fluid Boussmesq Rayleigh-Taylor instability and transition to turbulence are used to investigate Rayleigh-Taylor turbulence. The Schmidt, Atwood and bulk Reynolds numbers are Sc = 1. A = 0.01, Re less than or equal to 3000. High-Reynolds-number moment self-similarity, consistent with the the energy cascade interpretation of dissipation, is used to analyse the DNS results. The mixing layer width obeys a differential equation with solution h(t - C-o, h(0)) = (1)/(4)C(o)Agt(2) + rootAgC(o)h(0)(1/2) t + h(0); the result for h(t; C-o, h(0)) is a rigorous consequence of only one ansatz, self-similarity. It indicates an intermediate time regime in which the growth is linear and the importance of a virtual origin. At long time the well-known h similar to (1)/(4)C(o)Agt(2) scaling dominates. The self-similar analysis indicates that the asymptotic growth rate is not universal. The scalings of the second-order moments, their dissipations, and production-dissipation ratios, are obtained and compared to the DNS. The flow is not self-similar in a conventional sense there is no single length scale that scales the flow. The moment similarity method produces three different scalings for the turbulence energy-containing length scale, e, the Taylor microscale, lambda, and the Kolmogorov dissipation scale, eta. The DNS and the self-similar analysis are in accord showing l similar to Agt(2), lambdasimilar tot(1/2) and etasimilar to((A(2)g(2)/v(3))t)(-1/4) achieving self-similar behaviour within three initial eddy turnovers of the inception of the turbulence growth phase at bulk Reynolds numbers in the range of Re = 800-1000 depending on initial conditions. A picture of a turbulence in which the largest scales grow, asymptotically, as t(2) and the smallest scales decrease as t(-1/4), emerges. As a consequence the bandwidth of the turbulence spectrum grows as t(9/4) and is consistent with the R-t(3/4) Kolmogorov scaling law of fully developed stationary turbulent flows. While not all moments are consistent, especially the dissipations and higher-order moments in the edge regions, with the self-similar results it appears possible to conclude that: (i) the turbulence length scales evolve as a power of h(t; C-o, h(0)); (n) alpha, as demonstrated mathematically for self-similar Rayleigh-Taylor turbulence and numerically by the DNS, is not a universal constant; (111) there is statistically significant correlation between decreasing a and lower low-wavenumber loading of the initial spectrum.