Applying Statistical State Dynamics to Explain Spontaneous Shear/Buoyancy Layering in Stratified Turbulence

应用统计状态动力学解释层状湍流中的自发剪切/浮力分层

• 批准号: 1640989
• 负责人: Brian Farrell
• 金额: $ 50.67万
• 依托单位: Harvard University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-05-15 至 2022-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1640989&HistoricalAwards=false
• 关键词: Applying; Statistical; State; Dynamics; Explain

This research aims at advancing a new approach to explaining formation of small-scale horizontal structure in the shear and buoyancy fields of stratified turbulence in the atmosphere based on direct solution of the statistical state dynamics (SSD) equations. Direct solution of the SSD equations is a new approach to investigating the dynamics of turbulent flows that makes accessible to study mechanisms and phenomena in the dynamics that are inaccessible to analysis based on simulations of individual turbulent state realizations or on statistical mean quantities obtained by averaging ensembles of individual turbulent state realizations. Illustrative of such a mechanism is the cooperative instability of turbulence/mean-flow interaction that results in small scale shear and buoyancy layering in the stratified turbulence of both the atmosphere and ocean. This layering instability arises as an analytic bifurcation in the SSD of stratified turbulence while having no analytic counterpart in the dynamics of realizations, although the same layering phenomenon is seen in both SSD and realizations. In this research, SSD will be extended to obtain a theory for the spontaneous emergence of layering in the shear and buoyancy fields of stratified turbulence. The goal is to use SSD to understand the mechanism by which coherent layered structures are formed, maintained and equilibrated by interaction between the incoherent turbulence and the coherent layered structures.Intellectual Merit:The SSD method constitutes a conceptual as well as methodological advance in understanding turbulence in planetary atmospheres. By directly solving the statistical equations for the turbulent state dynamics the underlying coherent structures together with their associated incoherent eddy fields are obtained explicitly allowing e.g. analytic prediction of shear and buoyancy layer formation and of the sensitivity of the layer structure and its associated turbulent fluxes to changes in system parameters. Direct solution of the SSD equations reveals that shear/buoyancy layering and the associated turbulence is supported as a novel dynamical state in which coherent layered structures interact in a synergistic manner with small-scale turbulence to produce emergent layering instabilities leading to finite amplitude coherent equilibria in the shear/buoyancy/turbulence fields. The SSD approach allows exploration of these new cooperative dynamical regimes by providing analytic and numerical methods for obtaining turbulent statistical equilibria directly from the SSD of the turbulence.Broader Impacts:SSD allows analytical exploration of mechanisms by which coherent components of turbulence interact with incoherent components synergistically to produce emergent dynamical phenomena. The concepts and methods being developed are widely applicable to deepening understanding of turbulence in a wide variety of physical systems including mechanisms underlying formation and maintenance of coherent structures and regulation of turbulent transport in the atmosphere at all scales from the planetary to the boundary layer. SSD is broadly applicable to the study of a new class of emergent instabilities which are essentially related to mean flow/turbulence interaction but unrelated to laminar flow instability. Among other applications, this instability concept provides an explanation for the phenomenon of abrupt reorganization of atmospheric turbulence as a function of parameter change. Using SSD insight can be gained into the role of eddy fluxes in determining the climate response to boundary forcing (such as SST variation during ENSO events). This capability is important because the direct response to e.g. boundary condition changes can be small compared to the indirect effect brought about by subsequent changes induced in eddy statistics. SSD constitutes a general theory of turbulence in shear flow and among the broader impacts of this work are its application to turbulent phenomena in other physical contexts including plasma turbulence, the turbulence of wall-bounded shear flows and MHD turbulence. The broader impacts of this work also include support of a graduate student in atmospheric dynamics.

本研究旨在提出一种基于直接求解统计状态动力学(SSD)方程的新方法来解释大气分层湍流切变场和浮力场中小尺度水平结构的形成。直接求解SSD方程是研究湍流动力学的一种新方法，它使得研究动力学中的机制和现象变得容易，这些机制和现象无法基于单个湍流状态实现的模拟或通过平均单个湍流状态实现集合获得的统计平均值来进行分析。这种机制的例证是湍流/平均流相互作用的合作不稳定，导致大气和海洋的分层湍流中的小尺度切变和浮力分层。这种分层不稳定性是分层湍流的SSD中的一种解析分叉，而在实现的动力学中没有解析对应的分叉，尽管在SSD和实现中都可以看到相同的分层现象。在这项研究中，SSD将被扩展以获得分层湍流的剪切场和浮力场中的分层自发出现的理论。其目标是使用SSD来理解通过非相干湍流和相干层状结构之间的相互作用来形成、维持和平衡相干层状结构的机制。智力优点：SSD方法在理解行星大气中的湍流方面构成了概念和方法上的进步。通过直接求解湍流状态动力学的统计方程，显式地获得了基本的相干结构及其相关的非相干涡流场，从而可以解析地预测切变层和浮力层的形成，以及层结构及其相关的湍流通量对系统参数变化的敏感性。SSD方程的直接解表明，剪切/浮力分层和相关的湍流是一种新的动力学状态，在这种状态下，相干层状结构与小尺度湍流以协同方式相互作用，产生紧急分层不稳定性，导致剪切/浮力/湍流场中的有限振幅相干平衡。SSD方法可以通过提供直接从湍流的SSD获得湍流统计平衡的解析和数值方法来探索这些新的合作动力机制。广泛的影响：SSD允许对湍流的相干分量与非相干分量协同作用以产生紧急动力学现象的机制进行分析探索。正在开发的概念和方法广泛适用于加深对各种物理系统中的湍流的了解，包括形成和维持相干结构的基本机制以及从行星到边界层的所有尺度上对大气中湍流输送的调节。SSD可广泛应用于研究一类与平均流/湍流相互作用有关但与层流不稳定性无关的新的涌现不稳定性。在其他应用中，这个不稳定性概念解释了大气湍流作为参数变化的函数而突然重组的现象。使用SSD可以深入了解涡旋通量在确定气候对边界强迫的响应(如ENSO事件期间SST变化)中的作用。这种能力很重要，因为与涡旋统计中随后引起的变化所带来的间接影响相比，对例如边界条件变化的直接反应可能很小。SSD构成了剪切流中湍流的一般理论，这项工作的更广泛的影响包括它对其他物理环境中的湍流现象的应用，包括等离子体湍流、壁面剪切流的湍流和MHD湍流。这项工作的更广泛影响还包括对大气动力学研究生的支持。

项目成果

Statistical state dynamics analysis of buoyancy layer formation via the Phillips mechanism in two-dimensional stratified turbulence

二维分层湍流中浮力层形成的菲利普斯机制统计状态动力学分析

• DOI: 10.1017/jfm.2019.72
• 发表时间: 2019
• 期刊: Journal of Fluid Mechanics
• 影响因子: 3.7
• 作者: Fitzgerald, Joseph G.;Farrell, Brian F.
• 通讯作者: Farrell, Brian F.

Statistical state dynamics of vertically sheared horizontal flows in two-dimensional stratified turbulence

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
• 发表时间: 2018
• 期刊: Journal of Fluid Mechanics
• 影响因子: 3.7
• 作者: Fitzgerald, Joseph G.;Farrell, Brian F.
• 通讯作者: Farrell, Brian F.

Vertically Sheared Horizontal Flow-Forming Instability in Stratified Turbulence: Analytical Linear Stability Analysis of Statistical State Dynamics Equilibria

分层湍流中垂直剪切水平流动的不稳定性：统计状态动力学平衡的解析线性稳定性分析

• DOI: 10.1175/jas-d-18-0075.1
• 发表时间: 2018
• 期刊: Journal of the Atmospheric Sciences
• 影响因子: 3.1
• 作者: Fitzgerald, Joseph G.;Farrell, Brian F.
• 通讯作者: Farrell, Brian F.