A Model for Turbulence in Strongly Stratified Natural Flows

强分层自然流中的湍流模型

• 批准号: 1034221
• 负责人: Chris Rehmann
• 金额: $ 27万
• 依托单位: Iowa State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-09-01 至 2015-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1034221&HistoricalAwards=false
• 关键词: Model; Turbulence; Strongly; Stratified; Natural

To improve the modeling of turbulence and mixing in strongly stratified natural flows such as lakes and oceans, the proposed work involves developing an analytical model based on rapid distortion theory (RDT). Although turbulence can be intense in parts of natural flows, strong stratification can reduce vertical transport and mixing in the interior of lakes and oceans. Turbulence models based on the Reynolds-averaged Navier-Stokes (RANS) equations have provided useful predictions of stratified flows; however, they require adjustment to account for the interaction of internal waves and turbulence, and models that employ the gradient-transport assumption cannot predict upgradient fluxes, which can affect transport in strongly stratified flows significantly.In contrast to RANS models, RDT is naturally suited for predicting turbulence in a strongly stratified flow. While the gradient-transport approximation works best for a stratified flow when the time scales of the turbulence are much smaller than the time scale of gravitational adjustment (i.e., weak stratification), RDT applies when the stratification is strong. Although RDT does not predict the vortex mode seen at large times in some studies, it has successfully predicted many features of strongly stratified flows, including upgradient fluxes and preferential transport of temperature in a heat-salt system. The proposed work exploits this success to elucidate the physics and improve the modeling of strongly stratified flows.The objectives of the proposed work are to (1) apply RDT to homogeneous turbulence in strong stratification to determine (a) the mixing efficiency and its dependence on molecular diffusivity, (b) the effects of time-varying forcing in sheared and unsheared flows, and (c) the evolution of turbulence in a velocity and density field modeled after internal waves and (2) extend RDT to increase its relevance for natural flows by (a) applying it to a patch of turbulence with and without shear and (b) investigating the effect of moderate stratification and developing and testing a turbulence model based on RDT. Work for the first objective involves straightforward, though important, extensions of previous applications. Along with applying previous research on RDT for inhomogeneous turbulence to a stratified patch, work for the second objective involves relaxing the assumption of strong stratification by analytically evaluating the neglected nonlinear terms and adding a variable eddy diffusivity, which will be computed from the RDT solution, to extend the RDT to moderate stratification.The intellectual merit of the proposed work stems from the success of RDT in reproducing key features of several stratified flows and the PI?s experience with RDT and mixing in stratified flows in general. The theoretical problems are designed to answer key questions for stratified flows (objective 1) as well as relax the assumptions behind RDT to increase its applicability objective 2). Results from this research are expected to complement current models of stratified flows and offer insights on how to improve them. The broader impacts include training a graduate student; involving undergraduates from Iowa State University's Program for Women in Science and Engineering in the research; conducting outreach to schools; continuing collaborations with Drs. Hideshi Hanazaki, Hidekatsu Yamazaki, and William Merryfield; and improving the parameterization of sub-grid scale processes in models of lakes and oceans. The last of these will be aided by collaborating with Dr. Merryfield, an ocean modeler.

为了改进湖泊和海洋等强分层自然流中的湍流和混合建模，拟议的工作涉及开发基于快速畸变理论（RDT）的分析模型。尽管自然流的部分湍流可能很强烈，但强烈的分层会减少湖泊和海洋内部的垂直输送和混合。基于雷诺平均纳维-斯托克斯 (RANS) 方程的湍流模型提供了分层流的有用预测；然而，它们需要进行调整以考虑内波和湍流的相互作用，并且采用梯度传输假设的模型无法预测上升通量，这可能会显着影响强分层流中的传输。与 RANS 模型相比，RDT 自然适合预测强分层流中的湍流。当湍流的时间尺度远小于重力调整的时间尺度（即弱分层）时，梯度传递近似最适合分层流，而 RDT 适用于强分层。尽管 RDT 不能预测在一些研究中大量出现的涡流模式，但它已经成功预测了强分层流的许多特征，包括热盐系统中的梯度通量和温度优先传递。拟议的工作利用这一成功来阐明物理原理并改进强分层流的建模。拟议工作的目标是（1）将RDT应用于强分层中的均匀湍流，以确定（a）混合效率及其对分子扩散率的依赖性，（b）剪切和非剪切流中时变力的影响，以及（c） 在内波之后建模的速度和密度场，以及 (2) 扩展 RDT 以增加其与自然流动的相关性，方法是 (a) 将其应用于有和没有剪切的湍流斑块，以及 (b) 研究适度分层的影响并开发和测试基于 RDT 的湍流模型。第一个目标的工作涉及对先前应用程序的简单但重要的扩展。除了将先前针对非均匀湍流的 RDT 研究应用于分层斑块之外，第二个目标的工作涉及通过分析评估忽略的非线性项并添加可变涡流扩散率（将从 RDT 解计算）来放宽强分层的假设，以将 RDT 扩展到中等分层。所提出的工作的智力价值源于 RDT 在再现方面的成功 几种分层流的主要特征以及 PI 在 RDT 和混合分层流方面的经验。理论问题旨在回答分层流的关键问题（目标 1），并放宽 RDT 背后的假设以提高其适用性目标 2）。这项研究的结果预计将补充当前的分层流动模型，并提供有关如何改进这些模型的见解。更广泛的影响包括培养研究生；让爱荷华州立大学科学与工程女性项目的本科生参与这项研究；向学校进行外展活动；继续与博士合作。花崎英士、山崎英胜和威廉·梅里菲尔德；改进湖泊和海洋模型中子网格尺度过程的参数化。最后一项将通过与海洋建模师梅里菲尔德博士的合作来帮助完成。