An optimization approach for analysing nonlinear stability with transition to turbulence in fluids as an exemplar

R.R. Kerswell, Chris.C.T. Pringle, A.P. Willis

    Research output: Contribution to journalArticle

    47 Citations (Scopus)

    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
    Original languageEnglish
    Article number085901
    JournalReports on Progress in Physics
    Volume77
    Issue number8
    DOIs
    Publication statusPublished - 5 Aug 2014

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    Keywords

    • fluid mechanics
    • nonlinear
    • turbulence

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