The Geometry and Building Blocks of Chaotic Fluid Convection

混沌流体对流的几何结构和构建模块

• 批准号: 2151389
• 负责人: Mark Paul
• 金额: $ 30万
• 依托单位: Virginia Polytechnic Institute and State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-04-01 至 2025-03-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2151389&HistoricalAwards=false
• 关键词: Geometry; Building; Blocks; Chaotic; Fluid

Large systems containing fluids that are driven by an external source are at the core of many important challenges facing science and engineering today. Examples include weather prediction, the dynamics of the oceans, and turbulent flow in a pipe. The goal of this study is to build the insights that will be needed to describe, predict, and control systems such as these. The research will study these questions by focusing on the complex dynamics of a shallow layer of fluid that is heated from below. Dynamical systems theory will be used to provide a view into these dynamics by exploiting recent advances in algorithms and the availability of large supercomputing resources. This project will improve our understanding of the basic building blocks that compose chaotic fluid dynamics. This project will support undergraduate and graduate students, and the project will develop a new course for undergraduate engineering students on the exciting advances of dynamical systems and large-scale computations for important problems involving the dynamics of fluids. This study explores the basic nature of chaotic fluid dynamics using dynamical systems theory. The project focusses on the chaotic convection of a shallow layer of fluid that is heated from below in a gravitational field. This project builds an understanding of the fluid dynamics as a trajectory through a high-dimensional state space using the ideas of exact coherent structures and covariant Lyapunov vectors. Exact coherent structures are unstable and invariant solutions that provide a rigid skeleton in state space upon which the trajectory must navigate. The covariant Lyapunov vectors describe the growth or decay of small perturbations to the dynamics and quantify the unstable and stable manifolds of the dynamics. These quantities will be used to build an understanding of the geometry of state space and to identify the building blocks of the fluid motion. An important outcome will be the development of a statistical description of the dynamics based upon the gained insights. This project will provide important guidance for the development of theoretical ideas to describe a wide range of fluid systems, as well as other important large dissipative systems that are of societal interest.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.

当今科学和工程面临的许多重要挑战的核心是包含由外部来源驱动的流体的大型系统。例如，天气预测，海洋动力学以及管道中的湍流。 这项研究的目的是建立要描述，预测和控制此类系统的见解。 该研究将通过关注从下方加热的浅液层的复杂动力学来研究这些问题。动态系统理论将通过利用算法的最新进展和大型超级计算资源的可用性来提供对这些动态的看法。 该项目将提高我们对组成混沌流体动力学的基本构件的理解。该项目将支持本科生和研究生，该项目将开发一门新课程，以针对动态系统的令人兴奋的进步和大规模计算的新课程，以解决涉及流体动态的重要问题。 这项研究使用动力学系统理论探讨了混沌流体动力学的基本性质。 该项目的重点是从重力场下方加热的浅流体的混乱对流。 该项目使用精确的相干结构和协方差Lyapunov向量的思想，通过高维状态空间来建立对流体动力学作为轨迹的理解。确切的相干结构是不稳定且不变的解决方案，在状态空间中提供了固定的骨骼，轨迹必须在该空间上进行导航。协变量的lyapunov向量描述了小扰动对动力学的生长或衰减，并量化了动力学的不稳定和稳定的流形。 这些数量将用于建立对状态空间几何形状的理解，并确定流体运动的基础。 一个重要的结果将是基于获得的见解的动力学的统计描述。该项目将为制定理论思想的发展提供重要的指导，以描述广泛的流体系统，以及其他具有社会利益的重要大型耗散系统。该奖项反映了NSF的法定任务，并被视为值得通过评估的支持。利用基金会的知识分子和更广泛的影响审查标准。