Chaos and irreversibility of a flexible filament in periodically--driven Stokes flow

We use direct numerical simulations to solve for a filament (with bending modulus B, length L), suspended in a fluid (dynamic viscosity η), obeying Stokesian dynamics in a linear flow, γ˙=Ssin(ωt).The dynamical behavior is determined by the elasto-viscous number, μ≡(8πηSL4)/B and σ=ω/S. For a fixed σ, for small enough μ, the filament remains straight; as μ increases we observe respectively buckling, breakdown of time-reversibility and appearance of two-period and eventually chaotic spatiotemporal solutions. To analyze the dynamics of this non-autonomous system we consider the map obtained by integrating the dynamical equations over exactly one period. We find that this map has multiple fixed points and periodic orbits for large enough μ. For μ and σ within a certain range we find evidence of mixing of passive tracers.我们采用直接数值模拟（Direct Numerical Simulations）求解悬浮于动力粘度为η的流体中、弯曲模量为B且长度为L的细丝的运动，该系统遵循线性流场γ̇=Ssin(ωt)下的斯托克斯动力学（Stokesian dynamics）。其动力学行为由弹粘数μ≡(8πηSL⁴)/B与参数σ=ω/S共同决定。当σ固定时，若μ足够小，细丝将保持平直状态；随着μ增大，我们依次观测到屈曲、时间可逆性破缺、双周期解出现，最终演化至混沌时空解。为分析该非自治系统的动力学特性，我们考虑将动力学方程精确积分一个周期所得到的映射。研究发现，当μ足够大时，该映射存在多个不动点与周期轨道。当μ与σ处于特定区间时，我们观测到被动示踪剂（passive tracers）发生混合的相关证据。