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Reduced models in fluid dynamics via complex variable theory

通过复变量理论简化流体动力学模型

基本信息

批准号：
EP/I004920/1
负责人：
Darren Crowdy
金额：
$ 0.73万
依托单位：
Imperial College London
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2010
资助国家：
英国
起止时间：
2010 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FI004920%2F1
关键词：
Reduced models fluid dynamics via

项目摘要

Many emerging technologies involving microfluidics, MEMS (micro -electro-mechanical systems) and ``lab-on-chip'' design involve the control and manipulation of fluids at very small scales when the motion and dynamical mechanisms are very different to that of our day-to-day experience of fluids. Viscous, or frictional, effects dominate and lead to a range of new effects that need to be well understood. Such flows are referred to as Stokes flows or low Reynolds number flows. The same class of flows arise in understanding the motion of swimming microorganisms such as spermatozoa or E Coli bacteria. A wide range of experimentally observed behaviour associated with such swimming organisms remains to be properly explained and many of these phenomena have hydrodynamical underpinnings. This research aims to develop simple mathematical models, centred on the use of a powerful set of mathematical techniques from complex analysis, for understanding some of the hydrodynamical mechanisms. In particular, we will focus on how the presence of boundaries - such as no-slip walls where the fluid velocity must vanish or free surfaces on which surface tension is active - can affect the dynamical behaviour of the fluid or the swimming microorganisms.A second component of our project is to study reduced models, again using complex analysis, to understand the dynamics of vorticity when the fluid in which the vorticity is present is compressible. (Sound waves, for example, are a manifestation of a compressible fluid and their interaction with vortical structures associated with aircraft wakes is an important area of study in terms of minimizing noise pollution).

涉及微流体、MEMS（微机电系统）和“芯片实验室”设计的许多新兴技术涉及在非常小的尺度下对流体的控制和操纵，此时运动和动力机制与我们对流体的日常体验非常不同。粘性或摩擦效应占主导地位，并导致一系列新的效应，需要很好地理解。这种流动被称为斯托克斯流动或低雷诺数流动。在理解游动微生物（如精子或大肠杆菌）的运动时，也会出现同样的流动。实验观察到的与这种游泳生物相关的广泛行为仍有待适当解释，其中许多现象具有流体动力学基础。这项研究的目的是开发简单的数学模型，集中在使用一套强大的数学技术，从复杂的分析，了解一些流体动力学机制。特别是，我们将重点关注边界的存在-例如流体速度必须消失的无滑动壁或表面张力活跃的自由表面-如何影响流体或游泳微生物的动力学行为。我们项目的第二个组成部分是研究简化模型，再次使用复杂分析，了解当存在涡量的流体是可压缩的时涡量的动力学。（例如，声波是可压缩流体的一种表现形式，它们与飞机尾流相关的旋涡结构的相互作用是最大限度地减少噪音污染的重要研究领域）。