Background
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 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-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, which agrees more closely with experimental evidence than does a conventional stability analysis.
In the last decade, there has been a surge of interest in non-normal (also called non-modal) 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, the AIM Network has been created as a multi-disciplinary international network with both academic and industrial partners. The technical goals require a
broad range of expertise: mathematical, to retain the understanding developed for the canonical flows; numerical, to perform the high order computations
that are necessary when moving from simple to complicated flows; experimental, to assemble a catalogue of evidence that demonstrate when the technique
is more relevant than normal mode analysis. The network aims to expand to a broader industrial community as the ranges of applicability become clearer.
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