涡格中游泳者的捕获
Trapping of swimmers in a vortex lattice
摘要：
本文研究了刚性椭球体游泳者在二维定常涡流中的运动。在空间周期性阵列的漩涡游泳的数值模拟揭示了一系列可能的行为，包括捕获在一个单一的漩涡和运动引起的扩散在许多漩涡。虽然捕获概率消失在一个足够高的游泳速度，我们发现，它表现出令人惊讶的大振荡，因为这个临界游泳速度接近。引人注目的是，在更高的游泳速度下，我们发现游泳者垂直于他们的伸长方向游泳可能再次被困。为了解释这种复杂的行为，我们调查的游泳者相空间几何。我们确定的不动点和周期轨道的游泳者运动方程，调节游泳者被困在一个单一的漩涡细胞。对于低到中等的游泳速度，我们发现，一个稳定的周期性轨道包围不变的环面形成了一个运输障碍游泳者，并可以将他们困在个人的漩涡。对于游泳速度接近最大流体速度，我们发现，而不是垂直游泳者可以被困在渐近稳定的不动点。稳定的周期轨道和不动点的分岔分析解释了复杂的和非单调的崩溃和重新出现的游泳者捕获的游泳者的速度和形状是不同的。
英文摘要：
We examine the motion of rigid, ellipsoidal swimmers subjected to a steady vortex flow in two dimensions. Numerical simulations of swimmers in a spatially periodic array of vortices reveal a range of possible behaviors, including trapping inside a single vortex and motility-induced diffusion across many vortices. While the trapping probability vanishes at a sufficiently high swimming speed, we find that it exhibits surprisingly large oscillations as this critical swimming speed is approached. Strikingly, at even higher swimming speeds, we find swimmers that swim perpendicular to their elongation direction can again become trapped. To explain this complex behavior, we investigate the underlying swimmer phase-space geometry. We identify the fixed points and periodic orbits of the swimmer equations of motion that regulate swimmer trapping inside a single vortex cell. For low to intermediate swimming speeds, we find that a stable periodic orbit surrounded by invariant tori forms a transport barrier to swimmers and can trap them inside individual vortices. For swimming speeds approaching the maximum fluid speed, we find instead that perpendicular swimmers can be trapped by asymptotically stable fixed points. A bifurcation analysis of the stable periodic orbit and the fixed points explains the complex and non-monotonic breakdown and reemergence of swimmer trapping as the swimmer speed and shape are varied.
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