沉降柔性圈的稳定性
Stability of sedimenting flexible loops
摘要：
本文通过数值模拟和线性稳定性分析，研究了圆形柔性环在粘性流体中的沉降行为。数值模型涉及到一个本地细长体理论近似的流动耦合到欧拉-伯努利弹性力的不可伸展的纤维。从一个倾斜的圆开始，我们使用截断傅立叶模式来模拟动力学，以观察三种不同的运动状态：绝对稳定性，二维和三维动力学，这取决于弹性力和引力的相对重要性。我们确定的控制参数，并制定了一个简单的半解析稳定性判据，我们验证了数值。在所有情况下，沉降回路收敛到稳定的平面形状平衡，其中一个自由参数与纤维的初始条件和材料性质有关。
英文摘要：
We study the behaviour of circular flexible loops sedimenting in a viscous fluid by numerical simulations and linear stability analysis. The numerical model involves a local slender-body theory approximation for the flow coupled to the Euler-Bernoulli elastic forces for an inextensible fibre. Starting from an inclined circle, we simulate the dynamics using truncated Fourier modes to observe three distinct regimes of motion: absolute stability, two-, and three-dimensional dynamics, depending on therelative importance of elastic and gravitational forces. We identify the governing parameter and develop a simple semi-analytic stability criterion, which we verify numerically. In all cases, sedimenting loops converge to stable, planar shape equilibria with one free parameter related to the initial conditions and material properties of the fibre.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
