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仍然是定性层面的辩论主题。 然而，理论和实验之间的差距正在关闭由于最近发现的三维行波解的Navier-Stokes方程，最好的描述为精确的相干结构。本研究将继续研究和表征这些丰富的解决方案在平面剪切流，并试图阐明其不稳定性和混乱的湍流特性之间的联系。该方法是分支和动力系统理论应用于非线性偏微分方程的流体力学。剪切湍流是一种普遍存在的现象，它发生在简单流体（如空气和水）的流动中，也发生在生物和工业过程中出现的更复杂的流体中。湍流对流体流动的性质有着巨大的影响，例如动量和能量的传输以及燃烧、制造和环境中化学品的混合。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。这项研究有望提供一个基本的了解剪切湍流的性质，在很大程度上要归功于高性能的科学计算。将建立一个关于上述精确相干结构的数据库，并将其张贴在因特网上。

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.