Dias Frédéric, Vanden-Broeck Jean-Marc
Centre de Mathématiques et de Leurs Applications, Ecole Normale Supérieure de Cachan, 61 avenue du Président Wilson, 94235 Cachan cedex, France.
Philos Trans A Math Phys Eng Sci. 2002 Oct 15;360(1799):2137-54. doi: 10.1098/rsta.2002.1070.
Nonlinear waves in a forced channel flow of two contiguous homogeneous fluids of different densities are considered. Each fluid layer is of finite depth. The forcing is due to an obstruction lying on the bottom. The study is restricted to steady flows. First a weakly nonlinear analysis is performed. At leading order the problem reduces to a forced Korteweg-de Vries equation, except near a critical value of the ratio of layer depths which leads to the vanishing of the nonlinear term. The weakly nonlinear results obtained by integrating the forced Korteweg-de Vries equation are validated by comparison with numerical results obtained by solving the full governing equations. The numerical method is based on boundary integral equation techniques. Although the problem of two-layer flows over an obstacle is a classical problem, several branches of solutions which have never been computed before are obtained.
研究了在具有不同密度的两种相邻均匀流体的强迫通道流中的非线性波。每个流体层具有有限深度。强迫是由位于底部的障碍物引起的。研究限于稳定流。首先进行了弱非线性分析。在主导阶，该问题简化为一个强迫的科特韦格 - 德弗里斯方程，除了在层深度比的一个临界值附近，此时非线性项消失。通过将强迫的科特韦格 - 德弗里斯方程积分得到的弱非线性结果，与通过求解完整控制方程得到的数值结果进行比较来验证。数值方法基于边界积分方程技术。尽管两层流体在障碍物上流动的问题是一个经典问题，但还是得到了几个以前从未计算过的解分支。
