Doranehgard Mohammad Hossein, Karimi Nader, Borazjani Iman, Li Larry K B
Department of Mechanical and Aerospace Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong.
School of Engineering and Materials Science, Queen Mary University of London, London E1 4NS, United Kingdom.
Phys Rev E. 2024 Apr;109(4-2):045103. doi: 10.1103/PhysRevE.109.045103.
We numerically explore the two-dimensional, incompressible, isothermal flow through a wavy channel, with a focus on how the channel geometry affects the routes to chaos at Reynolds numbers between 150 and 1000. We find that (i) the period-doubling route arises in a symmetric channel, (ii) the Ruelle-Takens-Newhouse route arises in an asymmetric channel, and (iii) the type-II intermittency route arises in both asymmetric and semiwavy channels. We also find that the flow through the semiwavy channel evolves from a quasiperiodic torus to an unstable invariant set (chaotic saddle), before eventually settling on a period-1 limit-cycle attractor. This study reveals that laminar channel flow at elevated Reynolds numbers can exhibit a variety of nonlinear dynamics. Specifically, it highlights how breaking the symmetry of a wavy channel can not only influence the critical Reynolds number at which chaos emerges, but also diversify the types of bifurcation encountered en route to chaos itself.
我们通过数值模拟研究了二维、不可压缩、等温流体在波浪形通道中的流动，重点关注通道几何形状如何在雷诺数为150至1000之间影响通向混沌的路径。我们发现：（i）倍周期分岔路径出现在对称通道中；（ii）茹厄勒 - 塔肯斯 - 纽豪斯路径出现在非对称通道中；（iii）II型间歇性路径出现在非对称和半波浪形通道中。我们还发现，通过半波浪形通道的流动从准周期环面演变为不稳定不变集（混沌鞍点），最终稳定在周期为1的极限环吸引子上。这项研究表明，在较高雷诺数下的层流通道流动可以表现出多种非线性动力学。具体而言，它突出了打破波浪形通道的对称性不仅会影响混沌出现时的临界雷诺数，还会使通向混沌过程中遇到的分岔类型多样化。
