Stabilisation of exact coherent structures in fluid turbulence

流体湍流中精确相干结构的稳定性

• 批准号: EP/S037055/2
• 负责人: Dan Lucas
• 金额: $ 2.92万
• 依托单位: University of St Andrews
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2022
• 资助国家: 英国
• 起止时间: 2022 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FS037055%2F2
• 关键词: Stabilisation; exact; coherent; structures; fluid

The unpredictable and multi-scale nature of fluid turbulence makes it a significant modelling challenge for many industries and natural systems. From designing planes, trains and ships, renewable energy technologies to sustainable ventilation systems, the list of situations where turbulent flows are important is almost endless. This means that there are considerable economic opportunities associated with understanding and influencing turbulent flows. After many years of intense research there is yet to emerge a rigorous predictive theory for turbulence, despite progress in modelling and analysing the governing equations. The main reason for this difficulty lies in the complexity such flows exhibit in space and time. Temporal complexity is manifest via the chaotic nature of the solutions to the governing equations; the solutions never repeat and are sensitive to initial conditions. Spatial complexity appears as turbulence being more intense in some regions than others, for no appreciable reason. It is possible, though currently difficult, to extract from this complexity, simpler solutions which underly the turbulent state. These solutions may be steady in time or time periodic but crucially they are unstable, and therefore never fully realised. The hypothesis is that these solutions are good proxies for the turbulence from which we can glean new insights and make rigorous predictions of the flow. This project will provide a new computationally efficient method for predicting fluid turbulence by developing a control method to stabilise simple unstable solutions embedded in the chaos. Until now these solutions require careful convergence which is a two-step process; first a guess needs to be found, then the solution converged using a sophisticated numerical algorithm. Our approach is to include new terms into the governing equations which will 'passively' stabilise solutions enabling the evolution to tend towards them without the need for guesses or convergences. The increases in efficiency afforded by our new method will allow us to tackle vastly more complex scenarios than previously possible enabling us to approach the true "spatiotemporal complexity" of real world turbulence.

流体湍流的不可预测性和多尺度性质使其成为许多行业和自然系统的重大建模挑战。从设计飞机、火车和船舶，可再生能源技术到可持续通风系统，湍流的重要性几乎是无止境的。这意味着有相当多的经济机会与理解和影响湍流。经过多年的深入研究，尽管在建模和分析控制方程方面取得了进展，但仍然没有出现一个严格的湍流预测理论。这一困难的主要原因在于这种流动在空间和时间上表现出的复杂性。时间复杂性通过控制方程的解的混沌性质表现出来;解从不重复并且对初始条件敏感。空间复杂性表现为某些区域的湍流比其他区域更强烈，没有明显的原因。虽然目前很难，但从这种复杂性中提取出更简单的解决方案是可能的，这些解决方案是湍流状态的基础。这些解决方案可能是稳定的时间或时间周期，但至关重要的是，他们是不稳定的，因此从来没有完全实现。假设这些解是湍流的良好代表，我们可以从中收集新的见解并对流动进行严格的预测。这个项目将提供一个新的计算效率的方法来预测流体湍流通过开发一种控制方法来稳定简单的不稳定的解决方案嵌入在混乱。到目前为止，这些解决方案需要仔细收敛，这是一个两步的过程;首先需要找到一个猜测，然后使用复杂的数值算法收敛的解决方案。我们的方法是将新的条款纳入控制方程，这将“被动”稳定的解决方案，使演变倾向于他们，而不需要猜测或收敛。我们的新方法所提供的效率的提高将使我们能够处理比以前更复杂的场景，使我们能够接近真实的世界动荡的真正“时空复杂性”。

项目成果

Stabilization of exact coherent structures in two-dimensional turbulence using time-delayed feedback

使用延时反馈稳定二维湍流中的精确相干结构

• DOI: 10.1103/physrevfluids.7.014401
• 发表时间: 2022
• 期刊: Physical Review Fluids
• 影响因子: 2.7
• 作者: Lucas D