Willis, A.P., Kerswell, R.R. and Pringle, C.C.T. (2014) An optimization approach for analysing nonlinear stability with transition to turbulence in fluids as an exemplar. Reports on Progress in Physics, 77. 085901. ISSN 1361-6633
Abstract
This article introduces and reviews recent work using a simple optimization technique for analysing the nonlinear stability of a state in a dynamical system. The technique can be used to identify the most efficient way to disturb a system such that it transits from one stable state to another. The key idea is introduced within the framework of a finite-dimensional set of ordinary differential equations (ODEs) and then illustrated for a very simple system of two ODEs which possesses bistability. Then the transition to turbulence problem in fluid mechanics is used to show how the technique can be formulated for a spatially-extended system described by a set of partial differential equations (the well-known Navier–Stokes equations). Within that context, the optimization technique bridges the gap between (linear) optimal perturbation theory and the (nonlinear) dynamical systems approach to fluid flows. The fact that the technique has now been recently shown to work in this very high dimensional setting augurs well for its utility in other physical systems.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2014 IOP Publishing Ltd. This is an author produced version of a paper subsequently published in Reports on Progress in Physics. Uploaded in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 03 Jun 2015 09:59 |
Last Modified: | 17 Nov 2015 06:44 |
Published Version: | http://dx.doi.org/10.1088/0034-4885/77/8/085901 |
Status: | Published |
Publisher: | IOP Publishing |
Refereed: | Yes |
Identification Number: | 10.1088/0034-4885/77/8/085901 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:85948 |