Garnier J, Cherfils-Clérouin C, Holstein P-A
Laboratoire de Statistique et Probabilités, Université Paul Sabatier, 118 Route de Narbonne, 31062 Toulouse Cedex 4, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Sep;68(3 Pt 2):036401. doi: 10.1103/PhysRevE.68.036401. Epub 2003 Sep 12.
A weakly nonlinear model is proposed for the Rayleigh-Taylor instability in the presence of surface tension. The dynamics of a multimode perturbation of the interface between two incompressible, inviscid, irrotational, and immiscible fluids is analyzed. The quadratic and cubic nonlinear effects are taken into account. They include the nonlinear corrections to the exponential growths of the fundamental modulations. The role of the initial modulation spectrum is discussed. A saturation criterion in terms of the product of a local rms and a particular wave number is exhibited. It gives theoretical foundations for numerical conjectures and allows one to analyze the effects of fundamental parameters of the problem such as the dimension or the Atwood number.
针对存在表面张力时的瑞利 - 泰勒不稳定性，提出了一个弱非线性模型。分析了两种不可压缩、无粘性、无旋且不互溶流体界面的多模扰动动力学。考虑了二次和三次非线性效应。它们包括对基本调制指数增长的非线性修正。讨论了初始调制谱的作用。给出了一个基于局部均方根值与特定波数乘积的饱和准则。它为数值推测提供了理论基础，并能让人们分析问题的基本参数（如维度或阿特伍德数）的影响。
