CAREER: The restricted nonlinear framework: A new paradigm for modeling, analysis and control of wall-bounded turbulent flows

一个用于模拟、分析和控制壁面湍流流动的受限非线性框架项目将开发一套模型和工具来研究表面流动的特性。这些流动特性在运输应用中具有重要意义，在运输应用中，车辆表面和流经其上的空气之间的相互作用会导致摩擦阻力增加和相应的燃油效率降低。风力发电场是另一个相关的应用，在这种应用中，流经农场的空气与地面和风力涡轮机相互作用，导致流动模式，直接影响农场的效率。最新的流动物理数学模型往往是极其复杂和高维的，这使得它们很难分析，计算成本也很高。所得到的模型将用于研究流动现象，并提高某些最先进的计算工具的精度，这些工具使用流动的某些方面的模型来减少数值研究的计算负担。因此，巴尔的摩当地小学的外展活动以及JHU针对高中生的暑期计划将强调基础流体力学和可持续能源之间的联系，以便将他们正在学习的数学和科学放在紧迫的社会关切的背景下。该项目将开发一种新的降阶建模框架，旨在帮助克服描述壁面边界湍流的挑战，这一挑战因控制方程的分析复杂性和完全求解模拟的相关巨大计算成本而变得复杂。特别是，这项研究将开发核心理论和模拟工具，将约束非线性(RNL)建模原理扩展到大涡模拟(LES)、高雷诺数边界层流动和风电场流场的壁面模型。RNL模型是一种用于壁面湍流的降阶模型，它通过对Navier-Stokes(NS)方程的动力学限制而获得，从而导致简化的动力学和固有的降阶，从而大大降低了分析和计算的复杂性。这项工作的预期成果包括一套工具，用于(I)分析和隔离关键流动现象，(Ii)开发关键流动过程的机制模型，(Iii)提高大涡模拟的精度(通过RNL墙模型)，以及(Iv)设计基于模型的风电场控制策略。这项研究与一项教育和推广计划紧密结合在一起，该计划包括培训两名研究生，以及为中小学生开展活动，说明如何应用数学和科学来提高风能的效率。

A restricted nonlinear framework for modeling, analysis and control of wall-bounded turbulent flows project will develop a suite of models and tools for studying the characteristics of flow over surfaces. These flow properties have important implications in transport applications, where the interaction between the vehicle surface and the air flowing over it leads to increased friction drag and associated reductions in fuel efficiency. Wind farms are another related application, in which the air flowing over the farm interacts with both the ground and the wind turbines leading to flow patterns that directly impact the efficiency of the farm. The state-of-the-art mathematical models of the flow physics tend to be extremely complex and of high-dimension, which makes them hard to analyze and computationally expensive to simulate. The resulting models will be used to both study the flow phenomena, and to improve the accuracy of certain state-of-the-art computational tools that employ models of certain aspects of the flow to reduce the computational burden of numerical studies. Outreach activities at local Baltimore elementary schools and through a JHU summer program for high school students will therefore emphasize the connections between fundamental fluid mechanics and sustainable energy in order to put the mathematics and science they are learning in the context of pressing societal concerns. This project will develop a novel reduced order modeling framework that seeks to help overcome the challenges of characterizing wall-bounded turbulent flows, which is complicated by both the analytical intractability of the governing equations, and the associated large computational costs of fully resolved simulations. In particular, the proposed research will develop the core theory and simulation tools to extend restricted nonlinear (RNL) modeling principles to wall models for large eddy simulations (LES), high Reynolds number boundary layer flows and wind farm flow fields. The RNL model is a reduced-order model for wall-turbulence that is obtained through a dynamical restriction of the Navier-Stokes (NS) equations that leads to both simplified dynamics and an intrinsic order reduction, resulting in vastly reduced analytical and computational complexity. The expected outcomes of this work include a suite of tools for (i) analyzing and isolating key flow phenomena, (ii) developing mechanistic models of key flow processes, (iii) improving the accuracy of LES (through a RNL wall model), and (iv) designing model-based wind farm control strategies. The research is tightly coupled with an education and outreach plan that includes training of two graduate students as well as activities for elementary and high school students illustrating the application of mathematics and science to improve the efficiency of wind energy.