Modeling Coherent Structure in Convective Boundary Layers

对流边界层中的相干结构建模

• 批准号: 0514674
• 负责人: Ernest Agee
• 金额: $ 40.77万
• 依托单位: Purdue University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-09-01 至 2009-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0514674&HistoricalAwards=false
• 关键词: Modeling; Coherent; Structure; Convective; Boundary

The interest in the organized part of turbulent flows has increased considerably over the last thirty years. This is particularly true in atmospheric convective boundary layers, where observed fields of coherent structures (CSs) are seen to evolve from a background of microscale turbulent fluctuations. These CSs are viewed as fundamental building blocks that grow and interact to help establish more semi-permanent large-scale structures in atmospheric flows. CSs are fundamentally important to gaining an understanding of turbulence in general. In spite of observational successes, however, the problem of describing turbulent systems with coherent structures remains as a formidable theoretical challenge. In this research, low-order models (LOMs) for the dynamics of CSs in convective boundary layers will be developed. LOMs are commonly obtained by the Galerkin method and reveal basic mechanisms and their interplay through the focus on key elements, retaining only minimal number of degrees of freedom. In this method, fluid dynamical fields are expanded into infinite sets of time-independent basis functions; then projection of the original partial differential equations onto these functions yields a finite system of ordinary differential equations (the LOM) for the time evolution of the coefficients in truncated expansions. Following Lumley and coworkers, empirical orthogonal functions (EOFs) will be used as the basis functions. These will be computed from large eddy simulations (LES) and (potentially) observational data. This research will also solve two important problems that will allow more physically sound LOMs. These are: 1) The Galerkin method provides no guarantee against violations (in the LOM) of fundamental conservation properties of the original equations, which often results in unphysical behavior. 2) The EOFs are characteristics of the underlying probability distribution, estimated from data and, thus, subject to sampling errors. These should be appropriately quantified before interpreting and using sample EOFs. This will be accomplished by employing improvements over the traditional Galerkin approximations developed by the Co-PIs in their previous research. Broader impacts of the proposed activity The (re)discovery of CSs has led to questioning the relevance of the traditional statistical theory of turbulence. The problem of describing turbulent systems with coherent structures presents a formidable theoretical challenge. This research, resulting in relatively simple gyrostatic LOMs inherently possessing fundamental conservation properties of the fluid dynamic equations, will provide a new effective tool for scientific understanding of essential mechanisms and their interaction in CSs dynamics. This research should broadly impact the understanding of turbulent phenomena in general, as well as the intricacies of convective organization in atmospheric boundary layer flows. Further, this work impacts the general understanding of nature of the interacting roles of statistics and nonlinear dynamics.

在过去的三十年里，人们对湍流的有组织部分的兴趣大大增加。 在大气对流边界层中尤其如此，观察到的相干结构（CS）场是从微尺度湍流波动的背景演化而来的。 这些CS被视为基本构件，它们不断生长和相互作用，以帮助在大气流中建立更多半永久性的大型结构。 一般来说，CS 对于理解湍流至关重要。 然而，尽管观测取得了成功，描述具有相干结构的湍流系统的问题仍然是一个艰巨的理论挑战。在这项研究中，将开发对流边界层中 CS 动力学的低阶模型 (LOM)。 LOM 通常通过伽辽金方法获得，并通过关注关键元素来揭示基本机制及其相互作用，仅保留最少的自由度。 在该方法中，流体动力学场被扩展为无限组与时间无关的基函数；然后将原始偏微分方程投影到这些函数上，生成一个有限常微分方程组 (LOM)，用于截断展开式中系数的时间演化。 继 Lumley 和同事之后，经验正交函数 (EOF) 将被用作基函数。 这些将根据大涡模拟 (LES) 和（可能的）观测数据计算得出。这项研究还将解决两个重要问题，使 LOM 的物理性能更加健全。 它们是： 1) 伽辽金方法不能保证不违反（在 LOM 中）原始方程的基本守恒性质，这通常会导致非物理行为。 2) EOF 是基础概率分布的特征，是根据数据估计的，因此存在抽样误差。 在解释和使用示例 EOF 之前，应适当量化这些内容。 这将通过对 Co-PI 在之前的研究中开发的传统 Galerkin 近似进行改进来实现。拟议活动的更广泛影响 CS 的（重新）发现引发了人们对传统湍流统计理论的相关性的质疑。 用相干结构描述湍流系统的问题提出了巨大的理论挑战。 这项研究产生了相对简单的陀螺 LOM，其本质上具有流体动力学方程的基本守恒特性，将为科学理解 CS 动力学中的基本机制及其相互作用提供新的有效工具。 这项研究应该广泛影响对一般湍流现象以及大气边界层流中对流组织的复杂性的理解。 此外，这项工作影响了对统计和非线性动力学相互作用的本质的一般理解。