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

In 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.

Name dc:type.qualificationname

Doctor of Philosophy (PhD)

Level dc:type.qualificationlevel

Doctoral

Grantor dc:publisher.institution

University of Cambridge

Year dc:date.issued

2016

Author dc:creator

• Eaves, Thomas Scott

Advisor dc:contributor.advisor

• Caulfield, Colm

• Research Subject Categories::MATHEMATICS::Applied mathematics
• nonlinear stability
• stratified shear flows
• Couette flow
• transient growth phenomena
• adjoint based optimisation
• turbulence
• Koopman mode analysis
• Taylor instability

Licence

• https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/32046ab1-c93e-4a89-8e4f-2dd3aaac283e/download
• https://www.rioxx.net/licenses/all-rights-reserved/
• https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/98b8ea19-6939-409d-8579-4d126940e076/download

Language dc:language

en

Author Identifier

0000-0003-3473-1306

OAI identifier oai:identifier

oai:www.repository.cam.ac.uk:1810/260824