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

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方程的解决方案将被确定和不变的解决方案之间的过渡将被表征为湍流的非线性动力学提供一个粗略的全球描述。准二维流动在浅电解质层连续驱动的洛伦兹力提供了这种方法的理论，分析和实验发展的设置。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，牛顿和变分求解器将被用来发展这一观点，这将在实验中进行测试，在整个流域的流量可以测量的完整的空间和时间分辨率。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。虽然这项调查的重点是在两个维度上的流体湍流，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的心脏动力学（从轻度心律失常到潜在的致命性纤颤）。然而，最直接的实际应用是减少湍流阻力，这是汽车、航空和航运业消耗的很大一部分燃料。即使通过所提出的流动控制方法来逐步减少阻力，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提供，其中心目标是通过为最先进的数值算法提供有据可查、易于使用的接口，降低进入动力系统研究的门槛。

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.