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Efficient capture of the dominant periodic orbits underlying turbulent fluid flow.

有效捕获湍流流体流动的主要周期轨道。

基本信息

批准号：
EP/K03636X/1
负责人：
Ashley Willis
金额：
$ 8.4万
依托单位：
University of Sheffield
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2013
资助国家：
英国
起止时间：
2013 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FK03636X%2F1
关键词：
Efficient capture dominant periodic orbits

项目摘要

We are familiar with turbulence, through its affect on the stability of aircraft during flight. Fluids, in this case air, are generally regarded as exhibiting two states of flow - a 'laminar' state and a 'turbulent' state. Turbulence is characterised by chaotic variations in the direction of the flow, through the appearance of whirls or 'eddies'. In industrial applications, turbulence typically leads to a loss of performance, as significant energy can be lost to the generation of eddies. A typical example is in pipelines, important for domestic water supply, irrigation, cooling systems, oil and gas supply. Rather than energy being expended in moving fluid directly from A to B, almost all the energy is lost to the creation and sustenance of turbulence! The question of how to model turbulence, therefore, is consistently listed among the most important outstanding problems of applied mathematics and theoretical physics (e.g. http://en.wikipedia.org/wiki/List_of_unsolved_problems_in_physics). This work builds on recent progress in understanding turbulence, made possible by the recent discovery of solutions to the equations governing flow in pipes and channels. These solutions are in the form of waves. Although they travel with the flow, their structure is otherwise static in time. Turbulence is chaotic in time, however. A radical step-change in this approach will be to model turbulence in terms of solutions that vary in time and that repeat after a period of time. Substantially new computational methods will be required to isolate such solutions in the future. There is strong motivation for isolating repeating cycles, otherwise called periodic orbits - from dynamical systems theory they are known to efficiently capture complex dynamics, filtering out activity that is otherwise a distraction. Often only a handful of periodic orbits are required to reproduce the statistical properties of a seemingly complex system.By extracting periodic orbits directly from simulations of turbulence itself, this project aims to capture those periodic orbits that are dynamically most important. So far it has only been possible to find orbits via numerical continuation methods, where there is no clear link between the orbits and the actual dynamics of the system. Capturing periodic cycles in a 'large' system such as turbulence, however, has been a challenging task. In this work, a new symmetry projection method will be developed to enable meaningful visualisations of the underlying dynamics. It has been shown that this particular method dramatically improves our ability to spot recurring cycles, i.e. periodic orbits. Collaboration with a leading European experimental facility will enable further application of these methods, plus theoretically guided searches to be performed more rapidly than is possible in simulation.This work will have great impact on our understanding of dynamical processes underlying turbulence, where periodic orbits will provide a basis for describing and predicting fluid flow patterns. This will open new avenues of future research in methods of prediction and control.

我们熟悉湍流，因为它对飞行中飞机的稳定性有影响。流体，在这种情况下是空气，通常被认为表现出两种流动状态-"层流“状态和”湍流“状态。湍流的特征是在流动方向上的混乱变化，通过出现漩涡或“漩涡”。在工业应用中，湍流通常会导致性能损失，因为大量能量会损失在涡流的产生上。一个典型的例子是管道，对家庭供水，灌溉，冷却系统，石油和天然气供应很重要。与其说能量被消耗在直接将流体从A移动到B上，不如说几乎所有的能量都损失在湍流的产生和维持上了！因此，如何模拟湍流的问题一直被列为应用数学和理论物理学中最重要的突出问题之一（例如http：//en.wikipedia.org/wiki/List_of_unsolved_problems_in_physics）。这项工作建立在最近的进展，了解湍流，使最近发现的解决方案的方程在管道和渠道的流动。这些解是以波的形式存在的。虽然它们随流动而移动，但它们的结构在时间上是静态的。然而，湍流在时间上是混乱的。这种方法的一个根本性的步骤变化将是根据随时间变化并在一段时间后重复的解决方案来模拟湍流。未来将需要大量新的计算方法来隔离这些解决方案。有强烈的动机隔离重复的周期，也称为周期轨道-从动力系统理论，他们被称为有效地捕捉复杂的动态，过滤掉活动，否则是一个分心。通常只需要少量的周期轨道就可以重现看似复杂的系统的统计特性。通过直接从湍流本身的模拟中提取周期轨道，该项目旨在捕捉那些在动力学上最重要的周期轨道。到目前为止，只能通过数值延拓方法找到轨道，在轨道和系统的实际动力学之间没有明确的联系。然而，在“大”系统（如湍流）中捕获周期性循环一直是一项具有挑战性的任务。在这项工作中，将开发一种新的对称投影方法，使潜在的动力学有意义的可视化。已经表明，这种特殊的方法大大提高了我们发现重复循环的能力，即周期性轨道。与欧洲领先的实验设施的合作将使这些方法的进一步应用，加上理论指导的搜索，以更快地进行比可能在simulation.This工作将有很大的影响，我们了解的动力学过程的基础湍流，周期性轨道将提供一个基础，描述和预测流体流动模式。这将为未来的预测和控制方法研究开辟新的途径。