Exact Coherent Structures and the Nature Shear Turbulence

在过去的40年里，大量的实验和计算工作已经揭示了剪切湍流中复杂相干结构的存在和重要性。由于缺乏对这些结构的理论理解和基础，连贯结构的性质和作用在定性层面上仍然是争论的主题。然而，理论和实验之间的差距正在缩小，这要感谢最近发现的纳维-斯托克斯方程的三维行波解，它被最好地描述为精确的相干结构。本研究将继续研究和表征平面剪切流中这些丰富的解，并试图阐明它们的不稳定性与湍流特征的无序之间的联系。该方法是将分岔理论和动力系统理论应用于非线性流体动力学偏微分方程。将这些行波解扩展到管流和混合层。剪切湍流是一种普遍存在的现象，发生在简单流体的流动中，如空气和水，以及在生物和工业过程中出现的更复杂的流体。湍流对流体流动的性质有巨大的影响，例如动量和能量的传输以及燃烧、制造和环境中化学物质的混合。然而，湍流的复杂性严重限制了我们预测流体流动性质的能力。这项研究在很大程度上得益于高性能的科学计算，有望提供对剪切湍流本质的基本理解。将开发一个关于上述确切连贯结构的数据库，并在互联网上公布。

Over the past 40 years, substantial experimental and computational efforts have revealed the existence and importance of complex coherent structures in shear turbulence. The nature and role of the coherent structures have remained subjects of debate at a qualitative level due to a lack of theoretical understanding and foundation for these structures. However, the gap between theory and experiments is closing thanks to recent discoveries of three-dimensional traveling wave solutions of the Navier-Stokes equations that are best described as exact coherent structures. This research will continue the study and characterization of these rich solutions in plane shear flows and seek to elucidate the connections between their instabilities and the disorder that is characteristic of turbulence. The approach is that of bifurcation and dynamical systems theory applied to the nonlinear partial differential equations of hydrodynamics. Extensions of these traveling wave solutions to pipe flow and mixing layers will be considered.Shear turbulence is an ubiquitous phenomenon that occurs in the flow of simple fluids, such as air and water, and the more complex fluids that arise in biological and industrial processes. Turbulence has an enormous impact on the properties of fluid flows, such as the transport of momentum and energy and the mixing of chemicals in combustion, manufacturing and the environment. However, the complexity of turbulent flows severely limits our ability to predict the properties of fluid flows. This research promises to provide a fundamental understanding of the nature of shear turbulence thanks in large part to high-performance scientific computing. A database of the exact coherent structures mentioned above will be developed and posted on the Internet.