Passive scalars in complex fluid flows: variability and extreme events

复杂流体流动中的被动标量：变异性和极端事件

• 批准号: EP/I028072/1
• 负责人: Jacques Vanneste
• 金额: $ 40.08万
• 依托单位: University of Edinburgh
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2011
• 资助国家: 英国
• 起止时间: 2011 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FI028072%2F1
• 关键词: Passive; scalars; complex; fluid; flows

The transport and mixing of constituents in fluid flows is of central importance to many areas of sciences and engineering. Numerous industrial processes, for instance, involve the mixing and in many cases reactions of chemicals dissolved in fluids. Transport and mixing are also crucial to several environmental issues, such as the dispersion of pollutants and the distribution of atmospheric greenhouse gases. Often, the constituents do not affect the fluid flow: they are then regarded as passive scalars, which are transported (advected) by a given flow, mixed by molecular diffusion, and possibly react chemically. The evolution of their concentration is governed by the advection-diffusion-reaction equation. If the flow is known, this equation predicts how the scalar concentration varies in time and space. However, in many applications, the flows are chaotic and too complex to be known exactly. In this case, a probabilistic approach is needed which relates the statistics of the scalar concentration to the statistics of the fluid flows, modelled by random processes. This project will develop such an approach. Its main aim is to devise mathematical tools that make it possible to describe the range of scalar evolutions that can be expected from an ensemble of possible flows rather than the response to a single flow. Its novelty is to go beyond the standard description in terms of ensemble averages in order to fully characterise the variability of the concentration between different flow realisations. The outcomes of the project will be (i) new mathematical results that relate this variability to flow characteristics such as stretching properties, and (ii) new numerical methods, based on ensemble simulations, that sample the variability at minimal computational cost. Particular attention will be paid to rare events which lead to extreme values of the concentration. For example, when a scalar is released in a random flow, there is a small probability that it disperses only weakly and hence that its concentration remains high for a long time. Probabilities of this type have a clear practical importance, for instance for the assessment of the risk posed by pollution sources; their reliable estimation is one of the challenges addressed by the project. Three applications, all of them with environmental significance, have been chosen to serve as testbeds for the new developments. These involve: (i) water vapour, which condenses in low-temperature regions, (ii) ozone, which is depleted by its reaction with active chlorine, and (ii) phytoplankton, which experiences a logistic evolution while being advected. These applications are representative of a much broader class of problems, characterised by weak diffusion and well-mixed initial conditions, to which the methods devised can be applied. Beyond this, the results will be relevant to a number of other systems modelled by infinite-dimensional random dynamical systems.

流体流动中成分的传输和混合对于科学和工程的许多领域至关重要。例如，许多工业过程涉及溶解在流体中的化学物质的混合，并且在许多情况下涉及反应。运输和混合对于一些环境问题也至关重要，例如污染物的扩散和大气温室气体的分布。通常，这些成分不会影响流体流动：它们被视为被动标量，通过给定的流动传输（平流），通过分子扩散混合，并可能发生化学反应。它们浓度的演变由平流扩散反应方程控制。如果流量已知，该方程可以预测标量浓度随时间和空间的变化情况。然而，在许多应用中，流程是混乱且过于复杂的，无法准确了解。在这种情况下，需要一种概率方法，将标量浓度的统计数据与通过随机过程建模的流体流量的统计数据联系起来。该项目将开发这样一种方法。其主要目标是设计数学工具，使描述标量演化的范围成为可能，这些标量演化可以从可能的流的集合中而不是对单个流的响应中预期。其新颖之处在于超越了整体平均值的标准描述，以便充分表征不同流量实现之间的浓度变化。该项目的成果将是（i）将这种可变性与拉伸特性等流动特性联系起来的新数学结果，以及（ii）基于集成模拟的新数值方法，以最小的计算成本对可变性进行采样。将特别关注导致浓度极端值的罕见事件。例如，当标量在随机流中释放时，有很小的概率它仅微弱地分散，因此其浓度在很长一段时间内保持较高水平。这种类型的概率具有明显的实际重要性，例如用于评估污染源造成的风险；他们的可靠估计是该项目要解决的挑战之一。三个应用程序都具有环境意义，已被选为新开发的测试平台。这些涉及：（i）水蒸气，在低温区域凝结，（ii）臭氧，由于与活性氯反应而被消耗，以及（ii）浮游植物，在平流过程中经历物流演化。这些应用代表了更广泛的问题类别，其特征是弱扩散和充分混合的初始条件，所设计的方法可以应用于这些问题。除此之外，结果将与由无限维随机动力系统建模的许多其他系统相关。

项目成果

The effect of coherent stirring on the advection-condensation of water vapour.

• DOI: 10.1098/rspa.2017.0196
• 发表时间: 2017-06
• 期刊: Proceedings. Mathematical, physical, and engineering sciences
• 作者: Tsang YK;Vanneste J
• 通讯作者: Vanneste J

Front propagation in cellular flows for fast reaction and small diffusivity

细胞流中的前向传播可实现快速反应和小扩散率

• DOI: 10.48550/arxiv.1404.1010
• 发表时间: 2014
• 作者: Tzella A

Dispersion in the large-deviation regime. Part 1: shear flows and periodic flows

大偏差区域的分散。

• DOI: 10.1017/jfm.2014.64
• 发表时间: 2014
• 期刊: Journal of Fluid Mechanics
• 影响因子: 3.7
• 作者: Haynes P

Dispersion in the large-deviation regime. Part I: shear flows and periodic flows

大偏差区域的分散。

• DOI: 10.48550/arxiv.1401.6665
• 发表时间: 2014
• 作者: Haynes P

The effect of coherent stirring on the advection-condensation of water vapour

相干搅拌对水蒸气平流冷凝的影响

• DOI: 10.48550/arxiv.1703.06291
• 发表时间: 2017
• 作者: Tsang Y