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From Self-similar Solutions to Turbulent Cascades

从自相似解到湍流级联

基本信息

批准号：
2032657
负责人：
Roman Grigoriev
金额：
$ 32.27万
依托单位：
Georgia Tech Research Corporation
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2020
资助国家：
美国
起止时间：
2020-09-01 至 2024-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2032657&HistoricalAwards=false
关键词：
Self similar Solutions Turbulent Cascades

项目摘要

Turbulent fluid flows are both ubiquitous and immensely important in the modern society. They shape climate and weather, control transmission of many infectious diseases and the spreading of pollution, and determine the fuel-efficiency of our cars, airplanes, and ships. Yet, many of turbulent flows’ properties remain mysterious despite centuries of systematic research. In particular, we do not fully understand the principles that control the motion of fluids such at air and water at very small scales. As a result, despite continuing advances in computing power, numerical simulations resolving the small-scale structure of turbulent flows remains out of reach, limiting our ability to make sustained improvements in numerous civilian and military applications. This project harnesses recent numerical and theoretical advances to describe how fluid motions at one scale can generate motions at another (often much larger or much smaller) scale, yielding a hierarchy of eddies responsible for the unique and beautiful structure of fluid turbulence. This research project uses a combination of novel numerical methods and innovative theoretical approaches to addresses several fundamental problems in fluid turbulence that remain largely unsolved despite almost a century of concerted effort. One of the oldest, most fundamental, and least understood issues in fluid turbulence is the multi-scale structure of the flow at high Reynolds numbers. Such structure emerges due to cascades of various quantities, such as energy, vorticity, and helicity, describing the fluid flow. Our understanding of the physical mechanisms of respective cascades is very limited. For instance, it is not entirely clear what determines the direction of the cascades, i.e., whether the flux of a particular quantity is towards large scales (inverse cascade) or small scales (direct cascade). This project aims to develop a dynamical description of direct and inverse cascades in two spatial dimensions. Advanced numerical methods for finding self-similar solutions to inviscid governing equations are used to uncover the fundamental physical mechanisms describing scale interaction in fluid flows that is responsible for the multi-scale nature of developed turbulence. Established tools from dynamical systems theory are leveraged to develop a comprehensive quantitative theory of turbulent cascades that does not rely on unproven assumptions and approximations that underlie existing statistical theories of turbulence.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

湍流流动在现代社会中是一个普遍存在且非常重要的问题。它们影响着气候和天气，控制着许多传染病的传播和污染的扩散，决定着我们的汽车、飞机和轮船的燃油效率。然而，尽管有几个世纪的系统研究，湍流的许多性质仍然是神秘的。特别是，我们还没有完全理解在非常小的尺度上控制空气和水等流体运动的原理。因此，尽管计算能力不断进步，但解决湍流小尺度结构的数值模拟仍然遥不可及，限制了我们在许多民用和军事应用中进行持续改进的能力。该项目利用最近的数值和理论进展来描述一个尺度的流体运动如何在另一个尺度（通常更大或更小）产生运动，产生一个负责流体湍流独特而美丽的结构的漩涡层次。该研究项目采用新颖的数值方法和创新的理论方法相结合，以解决流体湍流中的几个基本问题，尽管近世纪的共同努力，这些问题在很大程度上仍未解决。流体湍流中最古老、最基本和最不为人所知的问题之一是高雷诺数下流动的多尺度结构。这种结构的出现是由于描述流体流动的各种量的级联，例如能量、涡度和螺旋度。我们对各个级联的物理机制的理解非常有限。例如，不完全清楚是什么决定了叶栅的方向，即，无论特定量的通量是朝向大尺度（逆级联）还是朝向小尺度（直接级联）。该项目旨在对两个空间维度的正叶栅和逆叶栅进行动态描述。先进的数值方法，寻找自相似的解决方案，无粘控制方程被用来揭示基本的物理机制，描述规模的相互作用，在流体流动中，是负责开发的湍流的多尺度性质。从动力系统理论建立的工具被用来开发一个全面的定量理论的湍流级联，不依赖于未经证实的假设和近似的基础上现有的统计理论turbulence.This奖项反映了NSF的法定使命，并已被认为是值得通过评估使用基金会的智力价值和更广泛的影响审查标准的支持。