On the existence of two-dimensional nonlinear steady states in plane Couette flow
On the existence of two-dimensional nonlinear steady states in plane Couette flow
复制标题
平面Couette流中二维非线性稳态的存在性
DOI：
10.1063/1.2753982
复制
发表时间：
2007
影响因子：
4.6
通讯作者：
F. Rincon
中科院分区：
文献类型：
--
作者：
F. Rincon
本文利用平面Poietille流或受保序恒等算子扰动的平面Couette流的同伦，重新研究了平面Couette流中二维定常非线性动力学问题.我们的结果表明，这是不可能获得的非线性平面Couette流的解决方案，报告的Cherhabili和Eurstein [Eur. J. Mech. B/Fluids 14，667（1995）]中描述的方法。我们还证明了Mehta和Healey [Phys. Fluids 17，094108（2005）]对于小的保序扰动获得的稳定解受到他们论文中使用的修改后的方程组的伪影的影响。然而，使用修改后的版本，他们的模型并没有帮助找到平面Couette流的解决方案，在消失的保序扰动的限制。平面Couette流中二维非线性定常状态的存在性问题至今尚未解决。
The problem of two-dimensional steady nonlinear dynamics in plane Couette flow is revisited using homotopy from either plane Poiseuille flow or from plane Couette flow perturbed by a small symmetry-preserving identity operator. Our results show that it is not possible to obtain the nonlinear plane Couette flow solutions reported by Cherhabili and Ehrenstein [Eur. J. Mech. B/Fluids 14, 667 (1995)] using their Poiseuille-Couette homotopy. We also demonstrate that the steady solutions obtained by Mehta and Healey [Phys. Fluids 17, 094108 (2005)] for small symmetry-preserving perturbations are influenced by an artefact of the modified system of equations used in their paper. However, using a modified version of their model does not help to find plane Couette flow solution in the limit of vanishing symmetry-preserving perturbations either. The issue of the existence of two-dimensional nonlinear steady states in plane Couette flow remains unsettled.