论文标题
二维Stokes流中的界面不稳定性：弱非线性分析
Interfacial instabilities in two-dimensional Stokes flow: a weakly nonlinear analysis
论文作者
论文摘要
通过二阶扰动模式耦合方法研究了带有注入和吸力的二维Stokes流量。我们检查了分隔两种粘性流体的最初圆形界面的时间依赖性干扰，并得出了描述界面扰动振幅演化的非线性微分方程系统。线性稳定性分析表明，注射诱导的扩展界面是稳定的，而被吸力驱动的收缩运动是不稳定的。奇怪的是，在线性水平上，这种吸力不稳定性与流体之间的粘度对比无关。但是，二阶结果讲述了一个不同的故事，并表明粘度对比在确定新兴界面模式的形状中起着关键作用。通过关注非线性效应的开始，我们能够提取有关粘度对比度和表面张力的任意值的图案形成结构最基本特征的宝贵信息。
Two-dimensional Stokes flow with injection and suction is investigated through a second-order, perturbative mode-coupling approach. We examine the time-dependent disturbance of an initially circular interface separating two viscous fluids, and derive a system of nonlinear differential equations describing the evolution of the interfacial perturbation amplitudes. Linear stability analysis reveals that an injection-induced expanding interface is stable, while a contracting motion driven by suction is unstable. Curiously, at the linear level this suction instability is independent of the viscosity contrast between the fluids. However, second-order results tell a different story, and show that the viscosity contrast plays a key role in determining the shape of the emerging interfacial patterns. By focusing on the onset of nonlinear effects, we have been able to extract valuable information about the most fundamental features of the pattern-forming structures for arbitrary values of viscosity contrast and surface tension.
