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Title: Rossby waves on shear flows and the noiseless generation of small scales
Author: Crick, Andrew Paul Richard
Awarding Body: University of Cambridge
Current Institution: University of Cambridge
Date of Award: 2006
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The framework of normal modes of a stable flow in a channel is reviewed: two kinds of modes, regular and singular, are found. This framework is then used to study an initial-value problem, with initial conditions consisting of super-­positions of singular modes. Theoretical predictions are made concerning the excitation of regular modes in certain special cases. Chapter 3 describes numerical simulations of the relevant equations, which are shown to be in agreement with our predictions. In chapter 4 we review previous studies of non linear critical layers, in particular the asymptotic Stewartson-Warn & Warn (SWW) solution, and the instability analysis by Killworth & McIntyre. We investigate the pos­sibility that small non linearities, inherent in the full asymptotic solution, but suppressed in the SWW solution, could grow and trigger the instability. These non linearities have exponentially small amplitudes, but we present a heuristic scaling argument to show that they could indeed grow fast enough to significantly affect the evolution of the flow. Chapter 5 describes the nu­merical methods that were used in high-precision simulations that resolve the unstable modes. Finally in chapter 6 we describe the results of these simulations. We use these to extrapolate the asymptotic limit considered by SWW, and show that indeed after a certain time, that we measure, the un­stable modes grow to large amplitudes, and that the SWW flow is no longer the correct leading-order solution after this time.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available