发表机构
Imperial College London（帝国理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文用弱非线性理论分析简单剪切流对随从力活性细丝自发动力学的影响，发现剪切抑制振荡并驱动从圆形到椭圆旋转、横向拍动直至稳态偏转的转变。
AI 中文摘要
我们采用弱非线性理论来研究外部施加的简单剪切流如何影响在斯托克斯流中变形的无惯性活性细丝自发动力学的起始。细丝一端夹持在壁上，其自由端受到沿切向施加的压缩“随从力”。通过扩展我先前对无剪切情况的弱非线性分析（J. Fluid Mech., 1007 A65, 2025），我们推导出一个广义振幅方程，该方程控制弱剪切下接近起始的动力学。对振幅方程的分析表明，除了引起稳态偏转外，剪切还抑制了细丝的内在振荡。这种抑制源于剪切与内在振荡之间微妙的非线性共振，随剪切速率的平方成比例变化，并且是各向异性的——在流动方向上比垂直于流动方向更强。在没有剪切的情况下，已知在临界随从力值处会同时出现稳定的旋转状态（其中细丝尖端在平行于壁的平面内描绘圆形轨道）和不稳定的平面拍动状态，通常在此阈值之上观察到圆形旋转。剪切打破了这种简并性，驱动了一系列动力学转变：从圆形旋转到椭圆形旋转，然后到横向拍动（垂直于剪切方向），最终到稳态偏转。
英文摘要
We employ weakly nonlinear theory to investigate how an externally imposed simple shear flow affects the onset of spontaneous dynamics of an inertialess active filament deforming in Stokes flow. The filament, clamped to a wall at one end, is subjected to a compressive "follower force" applied tangentially at its free end. By extending my earlier weakly nonlinear analysis of the shear-free case (J. Fluid Mech., 1007 A65, 2025), we derive a generalized amplitude equation governing the near-onset dynamics under weak shear. Analysis of the amplitude equation shows that, besides inducing a steady deflection, the shear damps the filament's intrinsic oscillations. This damping arises from a subtle nonlinear resonance between the shear and the intrinsic oscillations, scales quadratically with the shear rate, and is anisotropic---stronger in the flow direction than normal to it. Without shear, stable whirling states, where the filament tip traces a circular orbit in a plane parallel to the wall, and unstable planar-beating states are known to simultaneously emerge at a critical follower-force value, with circular whirling typically observed beyond this threshold. Shear breaks this degeneracy, driving a sequence of dynamical transitions: from circular to elliptical whirling, then to transverse beating (normal to the shear), and ultimately to steady deflection.
