The nonlinear dynamics of a two-sided collapsible channel flow is investigated by using an immersed boundary-lattice Boltzmann method. The stability of the hydrodynamic flow and collapsible channel walls is examined over a wide range of Reynolds numbers $Re$ , structure-to-fluid mass ratios $M$ and external pressures $P_e$ . Based on extensive simulations, we first characterise the chaotic behaviours of the collapsible channel flow and explore possible routes to chaos. We then explore the physical mechanisms responsible for the onset of self-excited oscillations. Nonlinear and rich dynamic behaviours of the collapsible system are discovered. Specifically, the system experiences a supercritical Hopf bifurcation leading to a period-1 limit cycle oscillation. The existence of chaotic behaviours of the collapsible channel walls is confirmed by a positive dominant Lyapunov exponent and a chaotic attractor in the velocity-displacement phase portrait of the mid-point of the collapsible channel wall. Chaos in the system can be reached via period-doubling and quasi-periodic bifurcations. It is also found that symmetry breaking is not a prerequisite for the onset of self-excited oscillations. However, symmetry breaking induced by mass ratio and external pressure may lead to a chaotic state. Unbalanced transmural pressure, wall inertia and shear layer instabilities in the vorticity waves contribute to the onset of self-excited oscillations of the collapsible system. The period-doubling, quasi-periodic and chaotic oscillations are closely associated with vortex pairing and merging of adjacent vortices, and interactions between the vortices on the upper and lower walls downstream of the throat.

中文翻译：

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在两侧可折叠通道流中过渡到混沌

采用浸入式边界格子玻尔兹曼方法研究了两侧可折叠通道流的非线性动力学。在广泛的雷诺数范围内检查了流体动力流动和可折叠通道壁的稳定性 $重新$ , 结构与流体的质量比 $M$ 和外部压力 $P_e$ . 基于广泛的模拟，我们首先描述了可折叠通道流的混沌行为，并探索了可能的混沌路径。然后，我们探索导致自激振荡发生的物理机制。发现了可折叠系统的非线性和丰富的动态行为。具体来说，系统经历了超临界 Hopf 分岔，导致周期 1 极限循环振荡。可折叠通道壁的混沌行为的存在由可折叠通道壁中点的速度 - 位移相图中的正主导 Lyapunov 指数和混沌吸引子证实。系统中的混沌可以通过倍周期和准周期分岔来实现。还发现对称性破坏不是自激振荡开始的先决条件。然而，质量比和外部压力引起的对称性破缺可能导致混沌状态。涡度波中不平衡的跨壁压力、壁惯性和剪切层不稳定性有助于可折叠系统的自激振荡的发生。倍周期、准周期和混沌振荡与相邻涡的涡配对和合并，以及喉部下游上下壁涡之间的相互作用密切相关。涡度波中的壁惯性和剪切层不稳定性有助于可折叠系统的自激振荡的开始。倍周期、准周期和混沌振荡与相邻涡的涡配对和合并，以及喉部下游上下壁涡之间的相互作用密切相关。涡度波中的壁惯性和剪切层不稳定性有助于可折叠系统的自激振荡的开始。倍周期、准周期和混沌振荡与相邻涡的涡配对和合并，以及喉部下游上下壁涡之间的相互作用密切相关。