Farrell B F, Gayme D F, Ioannou P J
Department of Earth and Planetary Sciences, Harvard University, Cambridge, MA 02138, USA
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA.
Philos Trans A Math Phys Eng Sci. 2017 Mar 13;375(2089). doi: 10.1098/rsta.2016.0081.
This paper reviews results obtained using statistical state dynamics (SSD) that demonstrate the benefits of adopting this perspective for understanding turbulence in wall-bounded shear flows. The SSD approach used in this work employs a second-order closure that retains only the interaction between the streamwise mean flow and the streamwise mean perturbation covariance. This closure restricts nonlinearity in the SSD to that explicitly retained in the streamwise constant mean flow together with nonlinear interactions between the mean flow and the perturbation covariance. This dynamical restriction, in which explicit perturbation-perturbation nonlinearity is removed from the perturbation equation, results in a simplified dynamics referred to as the restricted nonlinear (RNL) dynamics. RNL systems, in which a finite ensemble of realizations of the perturbation equation share the same mean flow, provide tractable approximations to the SSD, which is equivalent to an infinite ensemble RNL system. This infinite ensemble system, referred to as the stochastic structural stability theory system, introduces new analysis tools for studying turbulence. RNL systems provide computationally efficient means to approximate the SSD and produce self-sustaining turbulence exhibiting qualitative features similar to those observed in direct numerical simulations despite greatly simplified dynamics. The results presented show that RNL turbulence can be supported by as few as a single streamwise varying component interacting with the streamwise constant mean flow and that judicious selection of this truncated support or 'band-limiting' can be used to improve quantitative accuracy of RNL turbulence. These results suggest that the SSD approach provides new analytical and computational tools that allow new insights into wall turbulence.This article is part of the themed issue 'Toward the development of high-fidelity models of wall turbulence at large Reynolds number'.
本文回顾了使用统计状态动力学（SSD）获得的结果，这些结果证明了采用这种观点来理解壁面边界剪切流中的湍流的好处。本工作中使用的SSD方法采用了二阶封闭，该封闭仅保留流向平均流与流向平均扰动协方差之间的相互作用。这种封闭将SSD中的非线性限制为明确保留在流向恒定平均流中的非线性以及平均流与扰动协方差之间的非线性相互作用。这种动力学限制，即从扰动方程中去除明确的扰动-扰动非线性，导致了一种简化的动力学，称为受限非线性（RNL）动力学。RNL系统中，扰动方程的有限个实现集合共享相同的平均流，为SSD提供了易于处理的近似，SSD等同于无限个集合的RNL系统。这个无限个集合系统，称为随机结构稳定性理论系统，为研究湍流引入了新的分析工具。RNL系统提供了计算效率高的方法来近似SSD，并产生自维持湍流，尽管动力学大大简化，但仍表现出与直接数值模拟中观察到的定性特征相似的特征。给出的结果表明，RNL湍流可以由与流向恒定平均流相互作用的少至单个流向变化分量来支持，并且对这种截断支持或“带宽限制”的明智选择可用于提高RNL湍流的定量精度。这些结果表明，SSD方法提供了新的分析和计算工具，能够对壁面湍流有新的见解。本文是主题为“迈向大雷诺数下壁面湍流高保真模型的发展”的特刊的一部分。
