Statistical state dynamics of vertically sheared horizontal flows in two-dimensional stratified turbulence
Statistical state dynamics of vertically sheared horizontal flows in two-dimensional stratified turbulence
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二维分层湍流中垂直剪切水平流的统计状态动力学
DOI：
10.1017/jfm.2018.560
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发表时间：
2018
影响因子：
3.7
通讯作者：
Farrell, Brian F.
中科院分区：
文献类型：
--
作者：
Fitzgerald, Joseph G.;Farrell, Brian F.
强分层湍流的模拟经常显示出被称为垂直剪切水平流（VSHFs）的连贯大尺度结构。在垂直结构相似的二维（2D）和三维（3D）分层湍流中均可出现VSHFs。VSHF形成的机制尚不完全清楚。本文利用统计状态动力学（SSD）研究了二维Boussinesq分层湍流模型中VSHFs的形成和平衡。在SSD中，运动方程直接用湍流状态的统计变量表示。对二维湍流的限制促进了SSD在分析和计算上的应用，即S3T，其中SSD通过将水平平均结构方程与系综平均摄动协方差方程耦合来表示。与完全非线性模拟相比，二阶SSD通过二阶产生准确的统计数据。特别是，S3T捕获了在均匀大尺度随机激励维持的湍流模拟中看到的VSHF和相关密度层的自发出现。S3T系统的一个优点是可以解析地理解VSHF的形成机制，即突现的VSHF与随机激发的大尺度重力波之间的波均流相互作用。通过与全非线性仿真的比较，验证了S3T解能够准确预测VSHF的尺度选择、对随机激励强度的依赖以及非线性平衡结构。这些结果构成了VSHF形成的理论，适用于解释湍流射流（如海洋赤道深射流）的地球物理例子的模拟和观测。
Simulations of strongly stratified turbulence often exhibit coherent large-scale structures called vertically sheared horizontal flows (VSHFs). VSHFs emerge in both two-dimensional (2D) and three-dimensional (3D) stratified turbulence with similar vertical structure. The mechanism responsible for VSHF formation is not fully understood. In this work, the formation and equilibration of VSHFs in a 2D Boussinesq model of stratified turbulence is studied using statistical state dynamics (SSD). In SSD, equations of motion are expressed directly in the statistical variables of the turbulent state. Restriction to 2D turbulence facilitates application of an analytically and computationally attractive implementation of SSD referred to as S3T, in which the SSD is expressed by coupling the equation for the horizontal mean structure with the equation for the ensemble mean perturbation covariance. This second-order SSD produces accurate statistics, through second order, when compared with fully nonlinear simulations. In particular, S3T captures the spontaneous emergence of the VSHF and associated density layers seen in simulations of turbulence maintained by homogeneous large-scale stochastic excitation. An advantage of the S3T system is that the VSHF formation mechanism, which is wave–mean flow interaction between the emergent VSHF and the stochastically excited large-scale gravity waves, is analytically understood in the S3T system. Comparison with fully nonlinear simulations verifies that S3T solutions accurately predict the scale selection, dependence on stochastic excitation strength, and nonlinear equilibrium structure of the VSHF. These results constitute a theory for VSHF formation applicable to interpreting simulations and observations of geophysical examples of turbulent jets such as the ocean’s equatorial deep jets.
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