Coherent Structures, Self-Sustaining Process and Bifurcations in Shear Flows

[803685]基于对剪切流中基本的自我维持过程的理解，提出了一种计算剪切流（如平面Couette、平面Poiseuille和管道流）中隐藏有序状态的方法。对这些状态的认识为分析剪切流中湍流的发生提供了新的起点。本文将基于隐稳态的计算、局部稳定性的分析和控制数值模拟，对导致湍流的分岔序列进行完整的描述。这些隐藏有序态与边界附近实验观察到的相干结构之间惊人的相似性将被研究。还建议开发自我维持过程的简化模型，例如早期工作中开发的低阶模型。这项工作说明了高性能科学计算的独特能力。通过这种方法揭示的流动特征是无法通过任何其他手段获得的，包括分析或实验技术，甚至是数值模拟。这些特征是隐藏在湍流之下的秩序，对它们的阐释具有深刻的理论和实践意义。湍流是工程和地球物理环境中流体流动以及许多生物流动的定义特征。因此，对湍流基本认识的进展具有广泛的实际意义。这项研究的一个直接应用是开发鲁棒模型，用于预测和控制管道和通道以及机翼和表面的湍流，目的是减少阻力和噪音。

9803685WaleffeBuilding on an understanding of a fundamental self-sustaining process in shear-flows, an approach is developed to calculate hidden ordered states in shear flows such as plane Couette, plane Poiseuille and pipe flows. Knowledge of these states provides new starting points for the analysis of the onset of turbulence in shear flows. A complete characterization of the sequence of bifurcations leading to turbulence will be attempted based on the calculation of hidden steady states, analyses of their local stability properties and controlled numerical simulations. The striking similarity between those hidden ordered states and the coherent structures observed experimentally near boundaries will be investigated. It is also proposed to develop simplified models of the self-sustaining process, such as a low-order model developed in earlier work.This work illustrates the unique capabilities of high-performance Scientific Computing. The flow features that are revealed by this approach are not accessible by any other means, including analytical or experimental techniques or even numerical simulations. These features are the order hidden beneath the turbulence and their elucidation is of deep theoretical and practical interest. Turbulence is the defining characteristic of fluid flows in engineering and geophysical settings as well as of many biological flows. Therefore, progress in the fundamental understanding of turbulence is of wide-ranging practical relevance. A direct application of this research is to the development of robust models for prediction and control of turbulent flows in pipes and channels and over wings and surfaces, with an aim at drag and noise reduction.