CAREER: Modeling and Control of Solid-Fluid Interactions in Aquatic Locomotion

我们的教师早期职业发展(CALEAR)研究计划专注于开发理论和计算基础设施，以模拟鱼类运动中复杂的固体-流体相互作用。鱼类和鲸目动物通过有节奏的形状变化在水中以极大的灵活性和效率移动，这会在动物身体周围产生不稳定的流动(通常是通过身体的涡流)。人们普遍认为，但并不完全理解，鱼类利用水流的不稳定对它们有利，从而实现了令人印象深刻的水动力效率。这个研究项目将研究动物形态变化与周围环境之间的动态耦合。我们的方法是将经典的流体力学理论与几何力学、动力学系统、控制理论和计算的思想相结合，建立固体-流体运动的简化模型，使运动的基本原理更加透明。这些简化的模型将被用来分析与涡度相互作用的个体和鱼群的运动稳定性，从而解释涡度在水上运动和鱼类鱼群中的作用。这些模型还将用于设计控制和运动规划的策略，更具体地说，研究所需运动的最佳形状变形。除了我们在水上运动中固体-流体相互作用的建模和控制方面的直接贡献外，我们的努力还将为昆虫和鸟类运动等许多重要问题提供有价值的见解，并将使新的工程应用成为可能，例如设计以生物为灵感的车辆，通过其形状的波动来推进自己。我们的教育努力将集中在创造一个一体化的教育和研究环境，并在工程和数学之间架起一座桥梁。事实上，本科生和研究生(包括妇女和少数群体)的参与以及在期刊、会议和课堂上传播我们的研究成果将是这项研究努力的一个组成部分。

Our Faculty Early Career Development (CAREER) research program focuses on the development of theoretical and computational infrastructures for modeling complex solid-fluid interactions in fishlike locomotion. Fish and cetaceans move in water with great agility and efficiency through rhythmic shape changes which generate unsteady flow around the animal's body (typically vortical flow past the body). It is widely believed, but not fully understood, that fish exploit the unsteadiness in the flow to their advantage hence achieving impressive hydrodynamic efficiencies. This research program will study the dynamic coupling between the animal shape changes and the surrounding . Our approach is to combine the classical theory of fluid dynamics with ideas from geometric mechanics, dynamical systems, control theory and computation to build reduced models of the solid-fluid motion that make the underlying principles of locomotion more transparent. These reduced models will be used to analyze the stability of motion of both individual and schools of fish interacting with vorticity - thus explaining the role of vorticity in aquatic locomotion and fish schooling. These models will also be used to devise strategies for control and motion planning, more specifically, to investigate optimum shape deformations for a desired locomotion. In addition to our direct contribution to modeling and control of solid-fluid interactions in aquatic locomotion, our efforts will provide valuable insights into a number of important problems such as insect and birdlike locomotion and will enable novel engineering applications such as the design of biologically-inspired vehicles that propel themselves by undulating their shape. Our educational efforts will focus on creating an integrated education and research environment and on building a bridge between engineering and mathematics. Indeed, involvement of undergraduate and graduate students (including women and minorities) and dissemination of our research results in journals, conferences, as well as in the classroom will be an integral part of this research effort.