Swimming the Chaotic Seas: Invariant Manifolds, Tori, and the Transport of Swimmers in Fluid Flows

在混乱的海洋中畅游：不变流形、托里和流体流动中游泳者的传输

• 批准号: 2314417
• 负责人: Kevin Mitchell
• 金额: $ 40万
• 依托单位: University of California - Merced
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-08-01 至 2026-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2314417&HistoricalAwards=false
• 关键词: Swimming; Chaotic; Seas; Invariant; Manifolds

The dynamics and control of self-propelled bodies, from swarms of autonomous underwater vehicles (AUVs) and fish schools to populations of swimming bacteria, are of great interest to biophysics and engineering. Yet, while much work has focused on the collective behavior arising from interactions between individuals, less is known about the dynamics of these individuals in external, dynamically changing environments. This research will tackle the fundamental question of how isolated, self-propelled swimmers are transported in unsteady fluid flows. By leveraging tools from dynamical systems theory, such as those used in analyzing the propagation of reaction fronts in fluid flows, this project aims to create better understanding of the behavior of swimmers moving in realistic flows in nature and the laboratory. This work will educate and train the next generation of the scientific work force and will greatly impact the growth and educational mission of UC Merced, a university that was recently established in one of California's most economically challenged areas.Stable and unstable manifolds are critical structures that control the transport and mixing of passive particles in steady, time-independent flows. These manifolds both partition the fluid into vortex cells and control the transport between cells via “turnstile” lobes in the fluid. Lagrangian coherent structures (LCSs) provide an analogous framework in unsteady, aperiodic flows. The objective of this project is to adapt these theories to particles that are both advected by the fluid and propelled under their own power. Invariant manifolds and passive LCS are no longer the most relevant structures. Rather, swimming invariant manifolds (SwIMs), which depend explicitly on the swimming speed, along with SwIM edges and invariant tori, form key structures in the phase space. This research will: (i) investigate the role of these structures in both trapping swimmers and generating ballistic motion, (ii) explore the role of SwIMs on restricting and guiding transport in chaotic environments, (iii) develop a rigorous approach to account for swimmer noise in vortex flows, and (iv) connect these ideas to real-world organisms and flows through collaborations with experimentalists that study the transport of bacteria and algae in microfluidic flows.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.

自推进机构的动力学和控制，从成群的自主水下航行器（AUV）和鱼群到游泳细菌的种群，是生物物理学和工程学的极大兴趣。然而，虽然许多工作都集中在个体之间的互动所产生的集体行为，很少有人知道这些个人在外部动态变化的环境中的动态。这项研究将解决如何孤立的，自我推进的游泳运动员在不稳定的流体流动中运输的基本问题。通过利用动力系统理论中的工具，例如用于分析流体流动中反应前沿传播的工具，该项目旨在更好地理解自然界和实验室中现实流动中游泳者的行为。这项工作将教育和培训下一代科学工作者，并将极大地影响加州大学默塞德的发展和教育使命，这是一所最近在加州最具经济挑战性的地区之一成立的大学。稳定和不稳定的歧管是控制被动颗粒在稳定，不随时间变化的流动中的运输和混合的关键结构。这些歧管将流体分隔成涡旋单元，并通过流体中的“旋转门”叶控制单元之间的输送。拉格朗日拟序结构（LCS）提供了一个类似的框架，在非定常，非周期性流动。这个项目的目标是使这些理论适应于既被流体平流又被自身动力推动的粒子。不变流形和被动LCS不再是最相关的结构。相反，游泳不变流形（SwIM），这明确取决于游泳速度，沿着与SwIM边缘和不变环面，形成相空间中的关键结构。这项研究将：（i）研究这些结构在捕获游泳者和产生弹道运动中的作用，（ii）探索SwIM在混沌环境中限制和引导运输的作用，（iii）开发一种严格的方法来解释涡流中的游泳者噪声，以及（iv）将这些想法与真实的-通过与研究微流体流动中细菌和藻类运输的实验学家合作，研究世界生物和流动。该奖项反映了NSF的法定使命，通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。