Spatially localized two-dimensional finite-amplitude states in plane Couette flow
Spatially localized two-dimensional finite-amplitude states in plane Couette flow
复制标题
平面 Couette 流中的空间局域二维有限振幅态
DOI：
--
复制
发表时间：
1995
期刊：
影响因子：
--
通讯作者：
U. Ehrenstein
中科院分区：
文献类型：
--
作者：
A. Cherhabili;U. Ehrenstein
本研究的目的是寻找平面库埃特流中的二维有限振幅波。我们计算的起点是平面泊肃叶流中的二维行波，我们通过泊肃叶-库埃特族在数值上将其扩展到平面库埃特流极限。有趣的是，平面库埃特流的非线性状态采用空间局域（类孤立）驻波的形式。这给出了为什么之前计算平面库埃特流中二维波的尝试失败的一些解释。基于壁和通道半宽之间速度差的一半，这些状态存在的最低（临界）雷诺数接近 1500。空间局部扰动状态的存在对应于平面库埃特流实验中观察到的过渡的亚临界方面，计算的非线性平衡解有望代表二次不稳定性的新基本状态。
The objective of this investigation is to search for two-dimensional finite-amplitude waves in plane Couette flow. The starting point for our computations are two-dimensional travelling waves in plane Poiseuille flow which we extend numerically through the Poiseuille-Couette family to the plane Couette flow limit. Interestingly, the nonlinear states for plane Couette flow take the form of spatially localized (solitary-like) stationary waves. This gives some explanation why previous attempts to compute 2D waves in plane Couette flow failed. The lowest (critical) Reynolds number for the existence of these states, based on half the velocity difference between the walls and channel half-width, is close to 1500. The existence of spatially localized perturbed states corresponds to the subcritical aspect of transition observed in plane Couette flow experiments and the computed nonlinear equilibrium solutions hopefully represent a new basic state for secondary instabilities.