标题： 基于统计状态动力学的库埃特流中非线性作用的维持湍流的研究 显示英文标题

标题： Statistical State Dynamics Based Study of the Role of Nonlinearity in the Maintenance of Turbulence in Couette Flow

摘要： 虽然线性非正交性是外部驱动流将能量传递给维持湍流的扰动场的机制的基础，但非线性也被认为起着关键作用。 本研究的目标是更好地理解非线性在维持湍流中的作用。 本研究采用的方法是在库埃特流中实现统计状态动力学（SSD）闭合，该方法是纳维-斯托克斯方程在累积展开中的二阶形式，其中平均算子是流向平均。 扰动是从流向平均的偏差，识别出两种可能有助于维持这些扰动的机制。 这些是由于扰动与波动平均流之间的相互作用而产生的参数扰动增长，以及由于扰动场成分之间的非线性相互作用而产生的瞬态扰动增长。 通过比较在SSD中维持的湍流和在相关的直接数值模拟（DNS）中维持的湍流，其中这些机制被选择性地包含和排除，发现参数增长维持了湍流的扰动场，而通常被引用的由于非线性相互作用散射引起的扰动瞬态增长机制则被发现抑制了扰动增长。 除了验证参数机制在DNS中维持扰动外，还验证了李雅普诺夫向量是主导DNS中扰动能量和能量学的结构。 进一步验证了这些向量负责维持支撑自维持过程（SSP）的滚转环流，特别是维持支持参数扰动增长的波动条纹。 显示英文摘要

摘要： While linear non-normality underlies the mechanism of energy transfer from the externally driven flow to the perturbation field that sustains turbulence, nonlinearity is also known to play an essential role. The goal of this study is to better understand the role of nonlinearity in sustaining turbulence. The method used in this study is implementation in Couette flow of a statistical state dynamics (SSD) closure at second order in a cumulant expansion of the Navier-Stokes equations in which the averaging operator is the streamwise mean. The perturbations are the deviations from the streamwise mean and two mechanisms potentially contributing to maintaining these perturbations are identified. These are parametric perturbation growth arising from interaction of the perturbations with the fluctuating mean flow and transient growth of perturbations arising from nonlinear interaction between components of the perturbation field. By the method of comparing the turbulence maintained in the SSD and in the associated direct numerical simulation (DNS) in which these mechanisms have been selectively included and excluded, parametric growth is found to maintain the perturbation field of the turbulence while the more commonly invoked mechanism of transient growth of perturbations arising from scattering by nonlinear interaction is found to suppress perturbation growth. In addition to verifying that the parametric mechanism maintains the perturbations in DNS it is also verified that the Lyapunov vectors are the structures that dominate the perturbation energy and energetics in DNS. It is further verified that these vectors are responsible for maintaining the roll circulation that underlies the self-sustaining process (SSP) and in particular the maintenance of the fluctuating streak that supports the parametric perturbation growth.