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Title: Instabilities of rotating and unsteady flows
Author: Souza, Max Oliveira de
Awarding Body: University of Cambridge
Current Institution: University of Cambridge
Date of Award: 1998
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This dissertation is divided into two parts. The first part discusses the stability and breakdown of swirling flows. The second one deals with the stability of time periodic flows. Chapter 1 gives the background and reviews previous work in vortex breakdown. Chapter 2 deals with various aspects of axisymmetric breakdown. These include the study of basic states that do not support waves, and the role played by the downstream boundary conditions in steady solutions to the Euler equations. A description of the bifurcation diagram for pipes is presented, and we also show how the process of wave-steepening can lead to the formation of a highly oscillatory shock. In chapter 3, we study the weakly non-linear stability of trailing vortices. Following numerical calculations by Yang (1992), who found a viscous instability for arbitrary large values of the swirl at sufficiently large Reynolds number, we present an analysis for the steady states and their stability. We obtain fast-swirling, steady states, and study their linear stability to viscous centre-modes. For nearly neutral modes, we investigate their weakly nonlinear stability, accounting for non-parallel effects. Previous work on stability of time-periodic flows is reviewed in chapter 4. In chapter 5, we extend the critical-layer analysis by Lin (1955) to unsteady flows, and use it to investigate the stability of several oscillatory flows. For slightly oscillatory Plane-Poiseuille flow, the method is able to recover periodic modes (asymptotic Floquet modes for large Reynolds numbers). Nevertheless, the method fails for the Stokes layer; the reasons for such failure are discussed. Finally, we present in chapter 6 some results on the completeness of Floquet modes in channels.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available