Dynamic Barriers to Swimming Agents in Complex Fluid Flows

自行体在水环境中的运动、定向和控制是一个活跃的科学研究领域。这一领域显然具有重要的工程应用，例如，成群的自主水下航行器、无人机集合或游泳的微型机器人。这一领域对于理解游动生物的基本物理也很重要，例如细菌、幼虫，甚至人造胶体粒子。过去的许多研究集中在静止环境流体中物体(代理人)之间的相互作用；这些相互作用可能导致集体行为，如学校教育、群聚和群体结盟。然而，很少有研究探索由外部扰动引起的复杂流动中游泳剂的运动。目前的研究将探索孤立的自行式游泳药剂是如何在这样的水流中运输的。这对于理解“真实世界”中的游泳是很重要的，因为在“真实世界”中，游泳者经常遇到不可忽视的，甚至是湍流的背景流。这项工作旨在确定游泳者无法进入的区域，或者只有在很长一段时间后才能进入的区域。在许多情况下，这些区域是由几何障碍划定的，这些障碍不是由物理墙强加的，而是由游泳者的动态和水流之间的微妙相互作用引起的。这项工作将开发预测这些障碍存在的地方的技术。这些研究将与巴克内尔大学的一名研究人员合作进行，他正在对微流体中的细菌进行实验。几十年来，人们已经理解不变流形是控制被动示踪剂在表现出混沌平流的流体中传输的关键结构。最近，拉格朗日相干结构为非定常、非周期流动中的被动平流提供了一个类似的框架。这项研究的目的是将这些理论扩展到既在流体中平流又在其自身动力下推进的代理人。被动不变流形和拉格朗日相干结构不再是最相关的对象。相反，被称为游泳不变流形(游泳)的新对象似乎是关键结构，它明确地依赖于游泳速度。本研究将为游泳者开发理论框架，评估其对游泳者运输的重要性，并将该框架应用于各种场景，包括：(I)不同长宽比的游泳者；(Ii)稳定的、周期性的和非周期的流体流动；(Iii)2D和3D的流动；(Iv)双曲型和椭圆型流动；(V)游泳者方向上的随机效应的影响；以及(Vi)游泳者之间的相互作用。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

The motion, orientation, and control of self-propelled bodies in aqueous environments is an active field of scientific research. This field clearly has important engineering applications to, for example, swarms of autonomous underwater vehicles, collections of aerial drones, or swimming microrobots. This field is also important for understanding the fundamental physics of swimming organisms, such as bacteria, larvae, or even artificial colloidal particles. Many past studies focused on the interactions between bodies (agents) within a stationary ambient fluid; these interactions can lead to collective behavior like schooling, flocking, and group alignment. However, few studies have explored the motion of swimming agents in complicated flows that are caused by external disturbances. The current research will explore how isolated, self-propelled swimming agents are transported within such a flow. This is important for understanding swimming in the "real world", where swimmers often encounter nonnegligible, even turbulent, background flows. This work seeks to identify regions that are inaccessible to a swimmer, or accessible only after a long time. In many cases, these regions are delineated by geometric barriers that are not imposed by physical walls, but rather arise from subtle interactions between the dynamics of the swimmer and that of the flow. This work will develop techniques to predict where such barriers exist. These studies will be conducted in collaboration with a Bucknell University investigator, who is conducting experiments on bacteria in microfluidic flows.For several decades it has been understood that invariant manifolds are the critical structures controlling the transport of passive tracers in fluids exhibiting chaotic advection. More recently, Lagrangian coherent structures have provided an analogous framework for passive advection in unsteady, aperiodic flows. The objective of this research is to extend these theories to agents that are both advected in the fluid and propelled under their own power. The passive invariant manifolds, and Lagrangian coherent structures, are no longer the most relevant objects. Rather, new objects called swimming invariant manifolds (SwIMs), which depend explicitly on the swimming speed, appear to be the key structures. This research will develop the theoretical framework for SwIMs, assess their importance to the transport of swimmers, and apply this framework to various scenarios, including: (i) swimmers of differing aspect ratios; (ii) steady, periodic, and aperiodic fluid flows; (iii) flows in 2D and 3D; (iv) hyperbolic versus elliptic flows; (v) the influence of stochastic effects in the swimmer's direction, and (vi) interactions between swimmers.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.