Sohn Sung-Ik
Department of Mathematics, Kangnung National University, Kangnung 210-702, Korea.
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Jun;75(6 Pt 2):066312. doi: 10.1103/PhysRevE.75.066312. Epub 2007 Jun 25.
The analytic model for the evolution of single and multiple bubbles in Rayleigh-Taylor mixing is presented for the system of arbitrary density ratio. The model is the extension of Zufiria's potential theory, which is based on the velocity potential with point sources. We present solutions for a single bubble, at various stages, from the model and show that the solutions for the bubble velocity and curvature are in good agreement with numerical results. We demonstrate the evolution of multiple bubbles for finite density contrast and investigate dynamics of bubble competition, whereby leading bubbles grow in size at the expense of neighbors. The model shows that the growth coefficient alpha for the scaling law of the bubble front depends on the Atwood number and increases logarithmically with the initial perturbation amplitude. It is also found that the aspect ratio of the bubble size to the bubble height exhibits a self-similar behavior in the bubble competition process, and its values are insensitive to the Atwood number. The predictions of the model for the similarity parameters are in accordance with experimental and numerical results.
针对任意密度比系统，给出了瑞利 - 泰勒混合中单个和多个气泡演化的解析模型。该模型是祖菲里亚势理论的扩展，其基于具有点源的速度势。我们从模型中给出了单个气泡在不同阶段的解，并表明气泡速度和曲率的解与数值结果吻合良好。我们展示了有限密度对比度下多个气泡的演化，并研究了气泡竞争动力学，即领先气泡以牺牲相邻气泡为代价而增大尺寸。该模型表明，气泡前沿标度律的增长系数α取决于阿特伍德数，并随初始扰动幅度呈对数增加。还发现，在气泡竞争过程中，气泡尺寸与气泡高度的纵横比呈现自相似行为，其值对阿特伍德数不敏感。该模型对相似参数的预测与实验和数值结果一致。
