Modeling Coherent Structure in Convective Boundary Layers

在过去的三十年里，人们对湍流中有组织的部分的兴趣大大增加了。这在大气对流边界层中尤其如此，在那里可以看到相干结构(CS)的观测场是从微尺度湍流涨落的背景演变而来的。这些大气环流被视为基本的积木，它们不断增长并相互作用，以帮助在大气流动中建立更多半永久性的大规模结构。一般情况下，对于了解湍流来说，层流是非常重要的。然而，尽管观测上取得了成功，描述具有相干结构的湍流系统的问题仍然是一个巨大的理论挑战。在这项研究中，将发展低阶模式(LOM)，用于研究对流边界层中的涡旋动力学。LOM通常由Galerkin方法获得，通过对关键元素的关注来揭示基本机制及其相互作用，仅保留最少的自由度。在这种方法中，流体动力场被展开成与时间无关的无限基函数集，然后将原始的偏微分方程组投影到这些函数上，得到截断展开中系数的时间演化的有限常微分方程组(LOM)。在Lumley和同事之后，将使用经验正交函数(EOFs)作为基函数。这些数据将根据大涡模拟(LES)和(可能的)观测数据进行计算。这项研究还将解决两个重要问题，使更多的身体健全的LOM。它们是：1)Galerkin方法不保证(在LOM中)违反原始方程的基本守恒性质，这通常会导致非物理行为。2)EOFs是根据数据估计的基本概率分布的特征，因此容易受到抽样误差的影响。在解释和使用样本EOFs之前，这些都应该被适当地量化。这将通过改进Co-Pis在其先前的研究中开发的传统Galerkin近似来实现。提议的活动的更广泛的影响。(重新)发现涡旋涡旋已导致对传统的湍流统计理论的相关性提出了质疑。描述具有相干结构的湍流系统是一个巨大的理论挑战。这项研究使得相对简单的陀螺仪LOM具有流体动力学方程的基本守恒性，这将为科学理解CSS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的理解，以及对大气边界层流动中对流组织的错综复杂的理解。此外，这项工作影响了对统计学和非线性动力学相互作用的本质的一般理解。

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.