A Model for Turbulence in Strongly Stratified Natural Flows

为了改进湖泊和海洋等强分层自然水流中的湍流和混合的建模，拟议的工作涉及发展一个基于快速扭曲理论(RDT)的分析模型。尽管在部分自然水流中湍流可能会很强烈，但强烈的层化会减少湖泊和海洋内部的垂直输送和混合。基于雷诺平均Navier-Stokes(RANS)方程的湍流模型提供了有用的分层流动预测，但它们需要调整以考虑内波和湍流的相互作用，并且采用梯度输运假设的模型不能预测升级通量，这会显著影响强分层流动中的输运。与RANS模型相比，RDT模型自然适用于预测强分层流动中的湍流。当湍流的时间尺度远小于重力调整的时间尺度(即弱层化)时，梯度输运近似适用于分层流动，而RDT适用于层化较强的情况。虽然RDT不能预测一些研究中大量出现的涡旋模式，但它已经成功地预测了强分层流动的许多特征，包括热-盐系统中通量的升级和温度的优先输送。这项工作的目的是(1)将RDT应用于强层化中的均匀湍流，以确定(A)混合效率及其对分子扩散系数的依赖，(B)剪切和非剪切流动中时变强迫的影响，以及(C)湍流在模拟内波的速度和密度场中的演变以及(2)扩展RDT以增加其与自然流动的相关性，方法是(A)将其应用于有切变和无切变的湍流斑块，以及(B)研究中等层结的影响，并开发和测试基于RDT的湍流模式。实现第一个目标的工作包括对以前的应用程序进行简单而重要的扩展。除了将前人对非均匀湍流的RDT的研究应用到层结区域之外，第二个目标的工作还包括通过对被忽略的非线性项进行解析评估来放松强层化的假设，并添加一个从RDT解计算出的可变的涡扩散系数，从而将RDT扩展到中等层结。所提出的工作的理论价值来自于RDT成功地再现了几个层状流的主要特征，以及总体上RDT和分层流中的混合的Pi？S经验。这些理论问题旨在回答分层流动的关键问题(目标1)，并放宽RDT的假设以增加其适用性(目标2)。这项研究的结果有望补充目前的分层流动模型，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；对学校进行外联；继续与Hideshi Hanazaki博士、Hidekatsu Yamazaki博士和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。其中最后一个项目将通过与海洋建模专家梅里菲尔德博士的合作得到帮助。

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.