Overseas travel to India and France

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.