Nonlinear Dynamics of Fluid Mixing and Flow Separation

流体混合和流动分离的非线性动力学

• 批准号: 0404845
• 负责人: George Haller
• 金额: $ 23.77万
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-08-01 至 2007-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0404845&HistoricalAwards=false
• 关键词: Nonlinear; Dynamics; Fluid; Mixing; Flow

This proposal discusses the use of nonlinear dynamical systems theory in solving several long-standing problems of fluid mixing and flow separation. On the mathematical side, it will advance the theory of nonhyperbolic invariant manifolds, inertial manifolds, advection-diffusion and dynamo equations, finite-time invariant sets, stability of nonautonomous systems, and aperiodic averaging. On the fluid mechanical side, the proposed work will broaden the understanding of three-dimensional unsteady fluid separation, diffusive tracer mixing, the topology of three-dimensional vortices, and the origin of dynamo action in the induction equations.In a broader sense, the proposal describes new approaches to nonlinear dynamical phenomena in oceanic and aerodynamic flows. Such phenomena have traditionally been poorly understood, because advanced mathematical theories, notably dynamical systems theory, have been underutilized in their study. The investigator proposes new theoretical tools for describing how different substances mix, and how high-speed fluid separates from boundaries. The proposal discusses how the results can improve ocean feature detection and prediction, advance aerodynamic design and aviation technology, and impact the design of efficient chemical mixers.

本文讨论了非线性动力系统理论在解决流体混合和流动分离中几个长期存在的问题中的应用。在数学方面，它将推进非双曲不变流形、惯性流形、平流扩散和发电机方程、有限时不变集、非自治系统的稳定性和非周期平均的理论。在流体力学方面，所提出的工作将拓宽对三维非定常流体分离、扩散示踪剂混合、三维涡旋拓扑结构以及感应方程中发电机作用起源的理解。在更广泛的意义上，该建议描述了海洋和气动流动中非线性动力学现象的新方法。由于先进的数学理论，特别是动力系统理论在这些现象的研究中没有得到充分的利用，传统上对这些现象的理解很少。研究者提出了新的理论工具来描述不同的物质如何混合，以及高速流体如何从边界分离。该提案讨论了结果如何改进海洋特征检测和预测，推进气动设计和航空技术，并影响高效化学混合器的设计。