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.

为了提高湍流和混合在强烈分层的自然流动，如湖泊和海洋的建模，拟议的工作涉及开发一个基于快速畸变理论（RDT）的分析模型。虽然湍流在自然流动的某些部分可能很强烈，但强烈的分层可以减少湖泊和海洋内部的垂直运输和混合。基于雷诺平均纳维尔-斯托克斯（RANS）方程的湍流模型对分层流动提供了有用的预测;然而，它们需要进行调整以考虑内波和湍流的相互作用，并且采用梯度输送假设的模式不能预测梯度通量，这会显著影响强分层流中的输送。RDT自然适合于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时（即，弱分层），RDT在分层强时适用。虽然RDT不能预测在某些研究中大量出现的涡旋模式，但它成功地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的优先输送。本文利用这一成功来阐明强分层流动的物理机制并改进其模拟方法。本文的目标是（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系数的依赖性，（B）剪切和非剪切流动中时变强迫的影响，（c）内波后模拟的速度和密度场中湍流的演化;（2）通过（a）将RDT应用于有和无剪切的湍流斑块以及（B）研究了中等层结的影响，并开发和测试了基于RDT的湍流模式。第一个目标的工作涉及直接的，虽然重要的，以前的应用程序的扩展。沿着将先前关于非均匀湍流RDT的研究应用于分层斑块，第二个目标的工作包括通过分析评估被忽略的非线性项并添加可变涡流扩散率来放松强分层的假设，该可变涡流扩散率将从RDT解计算，将RDT扩展到中等分层。建议工作的智力价值源于RDT在再现几个分层流的关键特征方面的成功，PI？在分层流中的RDT和混合方面的经验。这些理论问题旨在回答分层流的关键问题（目标1），以及放松RDT背后的假设，以增加其适用性目标2）。这项研究的结果预计将补充目前的分层流模型，并提供如何改进它们的见解。更广泛的影响包括培训一名研究生;让来自爱荷华州州立大学的女性科学与工程项目的本科生参与研究;向学校进行推广;继续与Hideshi Hanazaki，Hidekatsu Yamazaki和William Merryfield博士合作;以及改进湖泊和海洋模型中次网格尺度过程的参数化。最后一项工作将得到海洋模型专家梅里菲尔德博士的协助。