In the last ten years there has been a surge of interest in non-modal analysis applied to standard problems in fundamental fluid mechanics. Even in simple flows, the behaviour predicted by these non-modal analyses can be completely different from - and far more accurate than - that predicted by conventional analyses, particularly for the types of flows found in industrial situations.The successful application of non-modal analysis to standard problems sets the scene for step changes in engineering practice. Nevertheless, some very significant challenges must be overcome. Firstly, the standard approach cannot handle the non-linear problems often found in engineering. Secondly, the standard approach is computationally expensive and cannot handle problems with many degrees of freedom. Thirdly, the standard approach deals with simple measures, such as kinetic energy density, while other measures are usually more pertinent for industrial situations. Encouragingly, applied mathematicians and engineers have made significant progress in all of these areas. This progress has revealed that a generalized formulation of the problem in terms of constrained optimization and variational methods, adapting and applying methods from the control and computational communities, will bridge the gap between standard flows and engineering problems.Our vision is that future generations of engineering Computational Fluid Dynamics (CFD) tools will contain modules that can perform non-modal analysis. If and when such analyses can be made practicable they are certain to change the way that engineers design fluid mechanical systems, such as combustion chambers, turbine blades, reaction chambers and ink jet printers. Furthermore, they can readily deal with transient effects and non-periodic time-varying base flows, which are often particularly relevant in engineering situations.This research will benefit UK industries that rely on the modelling and control of fluid mechanics and thermoacoustics. For example, the pharmaceutical industry will benefit from a better understanding of transition to turbulence and relaminarization in physiological flows, which is important for the application of drugs via the nose and upper airways; The gas turbine industry will benefit from being able to perform instant sensitivity analyses of their fuel injectors and to combine this with greater understanding of the thermo-acoustics that leads to combustion instability; and the wind turbine industry will benefit from an improved prediction of the sensitivity of an aerofoil to turbulence transition and results of exposure to a gust or to the wake of the preceding aerofoil.The investigators in this proposal are all founder members of the EPSRC-funded Advanced Instability Methods (AIM) Network, which was set up in January 2009 to explore the relevance of non-normal analysis to industrial problems. Through masterclasses and workshops in academia and industry and an increasing number of web-based resources, the network provides a route for dissemination and exploitation of this research.In summary, the objectives of this proposal are to bridge the gap between fundamental work and engineering practice, to embed these techniques in the engineering design cycle and to reinforce a growing centre of excellence within the UK in this area. The generalized framework proposed here, combined with two challenging engineering examples and the resources of the AIM Network, will make this possible and demonstrate it to a wider engineering community.