Overseas travel to India and France

在许多科学和工业情况下，预测流动或系统中的微小扰动是增长(不稳定)还是衰减(稳定)是很重要的。传统的方法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，这往往会给出不准确的结果。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(Re)数(即在所有速度下)都是稳定的。然而，在现实中，流动在Re~2000处变得湍流，这取决于外部噪声和管道的粗糙度。这种差异的产生是因为，在第三个空间维度上，模式是非正态的(即非正交的)。这意味着它们可以相互补充能量，不应分开考虑。这种不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导致强劲的瞬时增长。例如，在管流中，非正态分析预测，在Re~2000处，微小扰动将迅速发展为沿流方向的条纹，这与实验证据一致。在过去的十年里，人们对应用于基本流体力学的非正态稳定性分析的兴趣激增。这项建议的合作伙伴之一P.J.施密德在研究和宣传非正态对流体机械不稳定性的影响方面发挥了重要作用，并就这一主题写了一本非常有影响力的书。另一位合作伙伴R.I.Sujith在热声不稳定性的非正态方面开创了一些极具原创性的工作。他已经证明，热声系统可能是极不正常的，它们的行为并不总是能通过传统的稳定性分析得到很好的预测。这项提议的PI M.P.Juniper在这两个领域都有背景(燃烧和基本流动不稳定性)。他最近扩展了RIS的工作，将PJS在流体机械不稳定性方面使用的一些技术包括在内。这项提案的三个合作伙伴于2008年6月在法国举行了会议，并起草了进一步研究合作的计划。在这里提出访问的目的是开始这些项目中的第一个项目的工作，规划未来的研究方向，并概述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.