Cheng Baolian, Glimm J., Sharp D. H.
Applied Physics Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545.
Chaos. 2002 Jun;12(2):267-274. doi: 10.1063/1.1460942.
In this paper we formulate a model for the merger of bubbles at the edge of an unstable acceleration driven (Rayleigh-Taylor) mixing layer. Steady acceleration defines a self-similar mixing process, with a time-dependent inverse cascade of structures of increasing size. The time evolution is itself a renormalization group (RNG) evolution, and so the large time asymptotics define a RNG fixed point. We solve the model introduced here at this fixed point. The model predicts the growth rate of a Rayleigh-Taylor chaotic fluid mixing layer. The model has three main components: the velocity of a single bubble in this unstable flow regime, an envelope velocity, which describes collective excitations in the mixing region, and a merger process, which drives an inverse cascade, with a steady increase of bubble size. The present model differs from an earlier two-dimensional (2-D) merger model in several important ways. Beyond the extension of the model to three dimensions, the present model contains one phenomenological parameter, the variance of the bubble radii at fixed time. The model also predicts several experimental numbers: the bubble mixing rate, alpha(b)=h(b)/Agt(2) approximately 0.05-0.06, the mean bubble radius, and the bubble height separation at the time of merger. From these we also obtain the bubble height to the radius aspect ratio. Using the experimental results of Smeeton and Youngs (AWE Report No. O 35/87, 1987) to fix a value for the radius variance, we determine alpha(b) within the range of experimental uncertainty. We also obtain the experimental values for the bubble height to width aspect ratio in agreement with experimental values. (c) 2002 American Institute of Physics.
在本文中，我们构建了一个模型，用于描述不稳定加速度驱动（瑞利 - 泰勒）混合层边缘气泡的合并。稳定加速度定义了一个自相似混合过程，其中结构大小不断增加的结构会出现随时间变化的反向级联。时间演化本身就是一个重整化群（RNG）演化，因此长时间渐近行为定义了一个RNG不动点。我们在此不动点求解这里引入的模型。该模型预测了瑞利 - 泰勒混沌流体混合层的增长率。该模型有三个主要组成部分：在这种不稳定流动状态下单气泡的速度、描述混合区域集体激发的包络速度，以及驱动反向级联且气泡尺寸稳定增加的合并过程。当前模型在几个重要方面与早期的二维（2 - D）合并模型不同。除了将模型扩展到三维外，当前模型包含一个唯象参数，即固定时间处气泡半径的方差。该模型还预测了几个实验数值：气泡混合率，α(b)=h(b)/Agt(2)约为0.05 - 0.06，平均气泡半径，以及合并时气泡的高度间距。由此我们还得到了气泡高度与半径的纵横比。利用斯米顿和扬斯的实验结果（AWE报告编号O 35/87，1987）来确定半径方差的值，我们在实验不确定度范围内确定了α(b)。我们还得到了气泡高度与宽度纵横比的实验值，与实验结果相符。(c) 2002美国物理研究所。
