A study of how indicators for 2-D turbulence depend on the driving force in the Navier-Stokes equation

研究二维湍流指标如何取决于纳维-斯托克斯方程中的驱动力

• 批准号: 0511533
• 负责人: Michael Jolly
• 金额: $ 28.36万
• 依托单位: Indiana University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-06-01 至 2010-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0511533&HistoricalAwards=false
• 关键词: study; how; indicators; turbulence; depend

This project is focused on the discovery of driving forces that supportthe Kraichnan theory of 2-D fully developed turbulence. In recent workthe investigators and their collaborators have identified critical wavenumbers expressed as averages of different norms of the solution to theNavier-Stokes equations (NSE). These wave numbers provide necessary, andnearly sufficient conditions for the Kraichnan theory to hold. This teamhas also localized to some extent the global attractor of the NSE in aplane spanned by two of these norms (one being the energy), to helpunderstand which driving forces produce these conditions. The proposedwork will combine this analysis with computational optimization to zero inon such forces, and then study in detail the turbulent features theyproduce. The mathematical treatment of turbulence is largely driven bythe heuristic theories of Kolmogorov, Batchelor and Kraichnan. Theapproach taken in projecting the attractor however, seems to be entirelynew. The information provided by this analysis will guide thecomputational component which otherwise would be confronted with a vastlandscape of possible driving forces to consider.Turbulence is readily observed in three-dimensional physical spacedomains. Most people think of a bumpy plane rides (in this case thedomain is the volume around the airplane). Like the swirls generated byrocks in a stream, rapidly changing patterns form in the air around theplane. Turbulence theories do not attempt to predict the precisedevelopment of these patterns, but rather find (a) consistent laws whichdescribe how, on average, energy is transferred to smaller length scales,and (b) critical length scales at which this this phenomenon changes. True 2-D flows in nature are less prevalent. The most prominent example,the earth's atmosphere, is actually a thin 3-D domain, whose behaviorapproaches that of a 2-D flow. The fate of energy over different lengthscales is more complicated for 2-D flow, though that of 3-D flow is insome sense embedded into it. Though 2-D experiments are difficult tocarry out in the laboratory, they allow for much finer study on acomputer. Of all 2-D flows, the one studied in this project is arguablythe most amenable to analysis and efficient simulation. Yet it isfundamental, not only to 2-D and nearly 2-D flows such as the atmosphere,but also to 3-D turbulence due to universality.

该项目的重点是发现支持Kraichnan二维充分发展湍流理论的驱动力。 在最近的工作中，研究人员和他们的合作者已经确定了临界波数，表示为Navier-Stokes方程（NSE）解的不同范数的平均值。 这些波数为Kraichnan理论的成立提供了必要的、几乎充分的条件。 该团队还在一定程度上将NSE的全局吸引子定位在由两个规范（一个是能量）跨越的平面上，以帮助理解哪些驱动力产生这些条件。 本文将联合收割机与计算优化相结合，对这种力进行归零，然后详细研究它们产生的湍流特性。 湍流的数学处理在很大程度上是由Kolmogorov，Batchelor和Kraichnan的启发式理论驱动的。 然而，投影吸引子的方法似乎是全新的。 这一分析提供的信息将指导计算部分，否则将面临一个广阔的前景可能的驱动力考虑。湍流很容易观察到三维物理空间领域。 大多数人会想到颠簸的飞机（在这种情况下，域是飞机周围的体积）。 就像溪流中的岩石产生的漩涡一样，飞机周围的空气中形成了快速变化的图案。 湍流理论并不试图预测这些模式的精确发展，而是寻找（a）描述能量如何平均转移到较小长度尺度的一致定律，以及（B）这种现象发生变化的临界长度尺度。真正的二维流动在自然界中并不普遍。 最突出的例子是地球大气层，它实际上是一个薄的3-D域，其行为接近2-D流的行为。 对于二维流动来说，不同长度尺度上能量的命运更加复杂，尽管三维流动在某种意义上嵌入其中。尽管二维实验很难在实验室中进行，但它们允许在计算机上进行更精细的研究。 在所有的二维流动中，本项目所研究的流动无疑是最适合分析和有效模拟的。 然而，它是基本的，不仅二维和近二维流动，如大气，而且三维湍流由于普遍性。