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Generalised nonlinear stability of stratified shear flows: adjoint-based optimisation, Koopman modes, and reduced models

dc.creatorEaves, Thomas Scott
dc.date.accessioned2018-11-24T23:19:08Z
dc.date.available2016-10-19T13:55:58Z
dc.date.available2018-11-24T23:19:08Z
dc.date.issued2016-10-04
dc.identifierhttps://www.repository.cam.ac.uk/handle/1810/260824
dc.identifier.urihttp://repository.aust.edu.ng/xmlui/handle/123456789/3408
dc.description.abstractIn this thesis I investigate a number of problems in the nonlinear stability of density stratified plane Couette flow. I begin by describing the history of transient growth phenomena, and in particular the recent application of adjoint based optimisation to find nonlinear optimal perturbations and associated minimal seeds for turbulence, the smallest amplitude perturbations that are able to trigger transition to turbulence. I extend the work of Rabin et al. (2012) in unstratified plane Couette flow to find minimal seeds in both vertically and horizontally sheared stratified plane Couette flow. I find that the coherent states visited by such minimal seed trajectories are significantly altered by the stratification, and so proceed to investigate these states both with generalised Koopman mode analysis and by stratifying the self-sustaining process described by Waleffe (1997). I conclude with an introductory problem I considered that investigates the linear Taylor instability of layered stratified plane Couette flow, and show that the nonlinear evolution of the primary Taylor instability is not coupled to the form of the linearly unstable mode, in contrast to the Kelvin-Helmholtz instability, for example. I also include an appendix in which I describe joint work conducted with Professor Neil Balmforth of UBC during the 2015 WHOI Geophysical Fluid Dynamics summer programme, investigating stochastic homoclinic bifurcations.
dc.languageen
dc.publisherDepartment of Applied Mathematics and Theoretical Physics, University of Cambridge
dc.publisherUniversity of Cambridge
dc.publisherDepartment of Applied Mathematics and Theoretical Physics
dc.publisherSt John's College
dc.subjectResearch Subject Categories::MATHEMATICS::Applied mathematics
dc.subjectnonlinear stability
dc.subjectstratified shear flows
dc.subjectCouette flow
dc.subjecttransient growth phenomena
dc.subjectadjoint based optimisation
dc.subjectturbulence
dc.subjectKoopman mode analysis
dc.subjectTaylor instability
dc.titleGeneralised nonlinear stability of stratified shear flows: adjoint-based optimisation, Koopman modes, and reduced models
dc.typeThesis


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