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DynSyst_Special_Topics: Dynamics Of Turbulent Flow Via Unstable Exact Navier-Stokes Solutions: Connecting Theory & Numerics With Experiments

DynSyst_Special_Topics：通过不稳定精确纳维-斯托克斯解的湍流动力学：连接理论

基本信息

批准号：
1234436
负责人：
Roman Grigoriev
金额：
$ 36万
依托单位：
Georgia Tech Research Corporation
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2012
资助国家：
美国
起止时间：
2012-10-01 至 2017-09-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1234436&HistoricalAwards=false
关键词：
DynSyst_Special_Topics Dynamics Turbulent Flow Via

项目摘要

The objective of this research program is to develop and to test experimentally a revolutionary new approach to modeling and predicting two-dimensional turbulent flows. A set of weakly unstable invariant Navier-Stokes solutions will be identified and transitions between invariant solutions will be characterized to provide a coarse global description of the nonlinear dynamics of turbulent flow. Quasi-2D flow in a shallow electrolyte layer continually driven by Lorentz forces provides the setting for theoretical, analytic and experimental development of this approach. Novel and proven techniques, such as periodic orbit theory, group representation theory, Krylov-subspace numerical methods, Newton and variational solvers will be used to develop this viewpoint, which will be tested in experiments where the flow can be measured with full spatial and temporal resolution throughout the entire flow domain.If successful, the results of this research will impact several areas of science, engineering, and medicine. Although the focus of this investigation is on fluid turbulence in two dimensions, the proposed approach has the potential to provide new ways to model, and ultimately control, a wide range of spatiotemporally chaotic systems, such as magnetic confinement fusion reactors and abnormal cardiac dynamics (from mild arrhythmias to potentially lethal fibrillation). The most immediate practical application, however, is the reduction of turbulent drag responsible for a significant part of the fuel consumed in the automotive, aviation, and shipping industries. Even an incremental reduction of drag by the proposed flow control methodology would have a tremendous economic impact. All software and data produced by the research program will be made publicly available with a central aim of lowering the barrier of entry to dynamical systems research by providing well-documented, easy-to-use interfaces to state-of-the-art numerical algorithms.

本研究计划的目标是开发和实验测试一种革命性的新方法来模拟和预测二维湍流。一组弱不稳定不变的Navier-Stokes解将被识别，不变解之间的转换将被表征，以提供湍流非线性动力学的粗略全局描述。由洛伦兹力持续驱动的浅电解质层中的准二维流动为该方法的理论、分析和实验发展提供了条件。新的和成熟的技术，如周期轨道理论，群表示理论，krylov -子空间数值方法，牛顿和变分求解将用于发展这一观点，这将在实验中进行测试，在整个流域中可以用全空间和时间分辨率测量流。如果成功，这项研究的结果将影响科学、工程和医学的几个领域。尽管这项研究的重点是二维的流体湍流，但所提出的方法有可能提供新的方法来建模并最终控制广泛的时空混沌系统，如磁约束聚变反应堆和异常心脏动力学（从轻度心律失常到潜在的致命颤动）。然而，最直接的实际应用是减少湍流阻力，而湍流阻力是汽车、航空和航运行业消耗燃料的重要组成部分。即使是通过提出的流量控制方法来减少阻力，也会产生巨大的经济影响。该研究项目产生的所有软件和数据都将公开，其中心目标是通过为最先进的数值算法提供记录良好、易于使用的界面，降低进入动力系统研究的门槛。