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.

为了改善在湖泊和海洋等强烈分层的自然流中的湍流和混合的建模，提出的工作涉及基于快速失真理论（RDT）的分析模型。尽管湍流在自然流的一部分中可能是强烈的，但是强大的分层可以减少湖泊和海洋内部的垂直运输和混合。基于雷诺平均的Navier-Stokes（RANS）方程的湍流模型为分层流提供了有用的预测。但是，他们需要调整以说明内波和湍流的相互作用，并且采用梯度转移假设的模型无法预测升级通量，这可以显着影响强大的分层流中的运输。与RANS模型相比，RDT自然适合预测强烈分层的流量中的湍流。虽然当湍流的时间尺度小于重力调节的时间尺度（即弱分层）时，梯度传输近似最适合分层流动，但当分层强时，RDT适用。尽管在某些研究中，RDT无法预测在大量时间内看到的涡旋模式，但它成功地预测了强烈分层流的许多特征，包括升级通量和在热盐系统中温度的优先运输。提出的工作利用了这一成功来阐明物理学并改善强烈分层流的建模。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）（a）（a）（a）（a）依赖分子扩散性的混合效率及其依赖于时空的内部效果，（b）在跨越的内部构成式脉动效果，构成式呈脉动，构成式的脉络脉冲，构成式构成的效果（b）构成式呈脉冲，构成式构成式构成的效果，构成了跨度的效果。通过（a）将其应用于带有和没有剪切的湍流，并研究中等分层，开发和测试基于RDT的湍流模型，以（a）将其应用于带有和没有剪切的湍流，以（a）将其应用于带有和没有剪切的湍流，以扩展其与自然流的相关性，从而扩大了RDT的相关性，从而扩大了RDT的相关性，从而扩大了RDT的相关性。第一个目标的工作涉及先前应用的直接扩展，但很重要。在将先前的RDT研究应用于分层贴片中，第二个目标的工作涉及通过分析评估被忽视的非线性术语来放松强层的假设，并添加可变的涡流扩散率，并添加从RDT延伸到中等分层的倾斜度。通常，几个分层流的关键特征以及PI的RDT经验和在分层流中混合的经验。理论问题旨在回答分层流的关键问题（目标1），并放松RDT背后的假设以提高其适用性目标2）。这项研究的结果有望补充当前的分层流模型，并提供有关如何改进它们的见解。更广泛的影响包括培训研究生；涉及爱荷华州立大学在研究中针对科学与工程女性计划的大学生；向学校进行宣传；继续与Drs合作。 Hideshi Hanazaki，hidekatsu Yamazaki和William Merryfield；并改善湖泊和海洋模型中亚网格量表过程的参数化。其中最后一个将通过与海洋建模者梅里菲尔德博士合作来帮助。