标题： 平面Couette流中层流和混沌吸引子的联合约化模型 显示英文标题

标题： Joint Reduced Model for the Laminar and Chaotic Attractors in Plane Couette Flow

摘要： 我们使用谱子流形（SSM）理论开发了平面Couette流在Kreilos与Eckhardt（2012）研究的永久混沌状态下的低维降阶模型。 我们的三维模型通过将动力学限制到边缘状态的最慢混合模式SSM上获得。 我们展示了这导致了一个非线性模型，该模型能够准确重构单个轨迹，同时表示整个混沌吸引子和层流动力学。 此外，我们推导出了一个二维庞加莱映射，这使得能够快速计算嵌入混沌吸引子中的周期轨道。 显示英文摘要

摘要： We use the theory of spectral submanifolds (SSMs) to develop a low-dimensional reduced-order model for plane Couette flow in the permanently chaotic regime studied by Kreilos & Eckhardt (2012). Our three-dimensional model is obtained by restricting the dynamics to the slowest mixed-mode SSM of the edge state. We show that this results in a nonlinear model that accurately reconstructs individual trajectories, representing the entire chaotic attractor and the laminar dynamics simultaneously. In addition, we derive a two-dimensional Poincar\'e map that enables the rapid computation of the periodic orbits embedded in the chaotic attractor.