Overseas travel to India and France

在许多科学和工业情况下，重要的是预测流动或系统中的小扰动是否会增长（不稳定）或衰减（稳定）。传统的技术是将扰动分解成在两个空间维度上正常（即正交）的模式，并分别研究每个模式的增长。然而，这往往给出不准确的结果。作为一个简单的例子，该技术预测管道中的流动在所有雷诺数（Re）下（即在所有速度下）都是稳定的。然而，实际上，根据外部噪声和管道粗糙度的不同，雷诺数约为2000时，流动会变成湍流。这种差异的产生是因为在第三空间维度上，模式是非正交的。这意味着它们可以相互提供能量，不应单独考虑。这种非正常的行为往往会在科学家和工程师最感兴趣的中间时间引起强烈的瞬时增长。例如，在管流中，非正态分析预测，微小扰动将在Re ~ 2000时迅速发展成流向条纹，这与实验证据一致。在过去的十年里，人们对应用于基础流体力学的非正态稳定性分析产生了浓厚的兴趣。该提案的合作伙伴之一P. J.施密德（P. J. Schmid）在调查和宣传非正态性对流体力学不稳定性的影响方面发挥了重要作用，并就该主题撰写了一本非常有影响力的书。另一位合伙人，R。I. Sujith在热声不稳定性的非正态性方面开创了一些高度原创性的工作。他已经表明，热声系统可以是非常不正常的，他们的行为并不总是预测以及由一个传统的稳定性分析。该提案的PI，M。P. Juniper在这两个领域（燃烧和基本流动不稳定性）都有背景。他最近扩展了RIS的工作，包括PJS在流体力学不稳定性方面使用的一些技术。该提案的三个合作伙伴于2008年6月在法国举行会议，并起草了进一步研究合作的计划。这里建议的访问的目的是开始这些项目的第一个工作，规划未来的研究方向，并概述了一些潜在的博士项目。

In many scientific and industrial situations, it is important to predict whether a small perturbation in a flow or system will grow (unstable) or decay (stable). The conventional technique is to decompose the perturbation into modes that are normal (i.e. orthogonal) in two spatial dimensions and to study the growth of each mode separately. This, however, often gives inaccurate results. As a simple example, this technique predicts that the flow in a pipe will be stable at all Reynolds (Re) numbers (i.e. at all velocities). In reality, however, the flow becomes turbulent at Re ~ 2000, depending on external noise and the pipe's roughness.This discrepancy arises because, in the third spatial dimension, the modes are non-normal (i.e. non-orthogonal). This means that they can feed energy into each other and should not be considered separately. This non-normal behaviour often causes strong transient growth at the intermediate times that are of most interest to scientists and engineers. For instance, in pipe flow, a non-normal analysis predicts that tiny perturbations will rapidly develop into stream-wise streaks at Re ~ 2000, agreeing with experimental evidence. In the last ten years there has been a surge of interest in non-normal stability analyses applied to fundamental fluid mechanics. One of the partners in this proposal, P. J. Schmid, has been instrumental in investigating and publicising the effect of non-normality on fluid mechanical instabilities and has written a very influential book on the subject. Another of the partners, R. I. Sujith, has pioneered some highly original work on non-normality in thermo-acoustic instabilities. He has shown that thermo-acoustic systems can be extremely non-normal and that their behaviour will not always be predicted well by a conventional stability analysis. The PI of this proposal, M. P. Juniper, has a background in both of these areas (combustion and fundamental flow instability). He has recently extended the work of RIS to include some of the techniques used by PJS on fluid mechanical instabilities.The three partners of this proposal met in France in June 2008 and drafted plans for further research collaboration. The purpose of the visits proposed here is to start work on the first of these projects, to map out future research directions and to outline a number of potential PhD projects.