CAREER: Innovation in Turbulence Research and the Scientific Computing Curriculum

PI: Gibson, John f .提案号：1554149提议的研究重点是对导致湍流产生和维持的基本湍流现象进行计算和理论研究。提出的方法是对层流到湍流的过渡进行严格的数学处理，然后将这些概念扩展到完全的湍流。这项研究的结果可能会对湍流很重要的工程和技术应用产生影响，这意味着我们周围的大多数流动以及过程工业中的大多数流动。最近的研究表明，通过将Navier-Stokes方程的高分辨率数值模拟处理为非常高维的动力系统，可以精确地计算中等湍流剪切流的不稳定平衡、行波和周期轨道形式的精确相干结构。这些不变解捕获了自20世纪50年代以来在实验和模拟中观察到的相干结构的形式和行为，它们提出了一种利用动力系统理论的思想来利用湍流剪切流中固有的低维自组织结构的方法。提出的研究目标是将这些想法发展成对中等雷诺数下湍流结构和动力学的严格理解，并将这种方法的成功扩展到高雷诺数。本研究的具体目标是：(1)为压力驱动的通道流动建立一个从中等到高雷诺数的精确相干结构的综合数据库；(2)根据这些结构的动力学严格推导出定量准确和可预测的湍流剪切流降阶模型。这些目标的成功实现将形成对壁面切变流中动量和涡量传输以及湍流能量产生的精确时空理解的基础，并将展示精确相干结构和高维动力系统理论在分析湍流中的实用性。他们还计划使新罕布什尔州的计算数学课程现代化，并将Julia（在拟议的研究中使用的混合计算语言）的教学带入课堂。

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.