CAREER: Innovation in Turbulence Research and the Scientific Computing Curriculum

职业：湍流研究和科学计算课程的创新

• 批准号: 1554149
• 负责人: John Gibson
• 金额: $ 50万
• 依托单位: University of New Hampshire
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-08-01 至 2021-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1554149&HistoricalAwards=false
• 关键词: CAREER; Innovation; Turbulence; Research; Scientific

PI: Gibson, John F.Proposal Number: 1554149The proposed research is focused on the computational and theoretical investigation of the fundamental turbulent flow phenomena that lead to the generation and sustainment of turbulence. The proposed approach to this problem is a rigorous mathematical treatment for laminar-to-turbulence transition and then an extension of these concepts to fully turbulent flows. The results of this research could have an impact on engineering and technology applications where turbulence is important, and this means most of the flows that surround us and most of the flows in the process industry.Recent research has shown that exact coherent structures in the form of unstable equilibria, traveling waves, and periodic orbits can be computed precisely for moderately turbulent shear flows, by treating well-resolved numerical simulations of the Navier-Stokes equations as very high-dimensional dynamical systems. These invariant solutions capture the form and behavior of coherent structures observed in experiment and simulation since the 1950s, and they suggest an approach for leveraging ideas from dynamical systems theory to exploit the inherent low-dimensionality of self-organized structures in turbulent shear flows. The goals of the proposed research are to develop these ideas into a rigorous understanding of the structure and dynamics of turbulence at moderate Reynolds numbers, and to extend successes of this approach to high Reynolds numbers. Specific objectives of the proposed research are: (1) to develop a comprehensive database of exact coherent structures for pressure-driven channel flow, from moderate to high Reynolds numbers, and (2) to rigorously derive quantitatively accurate and predictive reduced-order models of turbulent shear flow based on the dynamics of these structures. Successful achievement of these objectives will form the basis for a precise spatiotemporal understanding of momentum and vorticity transport and turbulent energy production in wall-bounded shear flows, and will demonstrate the utility of exact coherent structures and high-dimensional dynamical systems theory in analyzing turbulence. There are also plans to modernize the computational mathematics curriculum in New Hampshire and bring the teaching of Julia (the hybrid computing language to be used in the proposed research) into the classroom.

主要研究者：吉布森，约翰F.建议编号：1554149拟议的研究是集中在基本的湍流现象，导致湍流的产生和维持的计算和理论研究。对这个问题提出的方法是严格的数学处理层流到湍流过渡，然后将这些概念扩展到完全湍流。这项研究的结果可能会对工程和技术应用产生影响，其中湍流是重要的，这意味着我们周围的大多数流动和过程工业中的大多数流动。最近的研究表明，对于中等湍流剪切流，可以精确计算以不稳定平衡，行波和周期轨道形式存在的精确相干结构，通过将Navier-Stokes方程的高分辨率数值模拟视为非常高维的动力系统。这些不变的解决方案捕获的形式和行为的相干结构观察到的实验和模拟自20世纪50年代以来，他们提出了一种方法，利用动力系统理论的思想，利用固有的低维的自组织结构在湍流剪切流。拟议的研究的目标是发展这些想法到一个严格的理解的结构和动力学的湍流在中等雷诺数，并延长这种方法的成功，高雷诺数。拟议的研究的具体目标是：（1）开发一个全面的数据库，精确的相干结构的压力驱动通道流，从中等到高雷诺数，（2）严格推导出定量准确和预测的降阶模型的湍流剪切流的动力学的基础上，这些结构。这些目标的成功实现将形成一个精确的时空了解的动量和涡量传输和湍流能量的生产在壁边界剪切流的基础上，并将展示精确的相干结构和高维动力系统理论在分析湍流的效用。还有计划使新罕布什尔州的计算数学课程现代化，并将Julia（拟议研究中使用的混合计算语言）的教学带入课堂。