Advanced Instability Methods (AIM) Network

In many scientific and industrial situations, it is important to predict whether a small perturbation in a flow will grow (unstable flow) or decay (stable flow). Industrial applications of stability theory include: the break-up of the jet in an ink-jet printer; large scale mixing in a combustion chamber; thermo-acoustic oscillation in a gas turbine; coupled mode flutter of a wind turbine and mixing in small channels for pharmaceutical applications. 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 decade, there has been a surge of interest in non-normal stability analysis within the applied maths community. It is widely thought that non-normality is the root cause of the transient behaviour of the simple flows they have analysed. The aim of this network is to accelerate its exploitation in more complex flows, particularly those with industrial relevance. Conventional stability analyses are currently applied to many industrial situations and, as for simple flows, could miss some of the most significant behaviour.Non-normal analyses, as well as being more accurate, also predict the regions of a flow that are most influential in creating a desired result, such as good mixing. With development, this information will allow engineers to design 'backwards' from an end result, rather than 'forwards' by trial and error. Our long term vision is that the next generation of Computational Fluid Dynamics tools will contain modules that can perform non-normal stability analysis. An important goal is to distinguish between the situations in which a non-normal analysis is required and those in which a conventional analysis is sufficient. We will do this both by reviewing the canonical flows, such as jets/wakes, pipe flow, boundary layers and thermo-acoustic oscillations in a Rijke tube, and by accelerating work on a number of industrial case studies.To achieve this, we will create a multi-disciplinary international network with both academic and industrial partners. The technical goals will require a broad range of expertise: mathematical, to retain the understanding developed for the canonical flows; numerical, to perform the high order computations that will be necessary when moving from simple to complicated flows; experimental, to assemble a catalogue of evidence that will demonstrate when the technique is more relevant than normal mode analysis. The network will expand to a broader industrial community as the ranges of applicability becomes clearer. Currently, several groups are working in this area but, in this relatively young field, there is little formal interaction between them. The network will build on the UK's traditional strength in flow instability and incorporate partners from India, where there has recently been some outstanding work in non-normal analysis. The network will start with one very significant overseas partner (Peter Schmid from Ecole Polytechnique, France) and expand internationally during the two year start-up period.