A Model for Turbulence in Strongly Stratified Natural Flows

为了改进强分层自然流（如湖泊和海洋）中湍流和混合的建模，提出的工作包括开发基于快速失真理论（RDT）的分析模型。虽然在部分自然流动中湍流可能很强烈，但强烈的分层可以减少湖泊和海洋内部的垂直输送和混合。基于reynolds -average Navier-Stokes （RANS）方程的湍流模型提供了有用的分层流预测；然而，它们需要调整以考虑内波和湍流的相互作用，而且采用梯度输运假设的模式不能预测上升梯度通量，而上升通量会显著影响强分层流中的输运。与RANS模型相比，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（即弱分层）时，梯度输运近似对分层流动最有效，而当分层较强时，RDT适用。虽然在一些研究中，RDT并不能预测大时间的涡旋模式，但它已经成功地预测了强分层流动的许多特征，包括热盐系统中的上升梯度通量和温度优先输运。提出的工作利用这一成功来阐明物理和改进强分层流动的建模。所提议的工作的目标是(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，(b)剪切和非剪切流动中时变强迫的影响，(c)在以内波为模型的速度和密度场中湍流的演变；(2)扩展RDT，通过(a)将其应用于有和没有剪切的湍流斑块；(b)研究适度分层的影响，开发和测试基于RDT的湍流模型，从而增加其与自然流动的相关性。实现第一个目标的工作包括对先前应用程序的直接扩展，尽管这很重要。除了将先前对非均匀湍流的RDT研究应用于分层斑块之外，第二个目标的工作包括通过解析评估被忽略的非线性项和添加一个可变涡流扩散系数（将从RDT解中计算）来放宽强分层的假设，从而将RDT扩展到中等分层。所提议的工作的智力价值源于RDT在再现几个分层流和PI的关键特征方面的成功。i’在分层流中进行RDT和混合的一般经验。理论问题旨在回答分层流动的关键问题（目标1），并放宽RDT背后的假设，以增加其适用性（目标2）。这项研究的结果有望补充当前的分层流模型，并为如何改进它们提供见解。更广泛的影响包括培养研究生；让爱荷华州立大学女性科学与工程项目的本科生参与研究；开展学校外展活动；继续与博士合作。花崎秀、山崎秀胜和威廉·梅里菲尔德；改进湖泊和海洋模式中亚网格尺度过程的参数化。最后一项工作将由海洋建模师梅里菲尔德博士协助完成。

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.