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Title: Nonlinear effects in two-dimensional separating-flow transition
Author: Vickers, Ian Paul
Awarding Body: University of London
Current Institution: University College London (University of London)
Date of Award: 1993
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In this thesis the main aim is to extend the theory governing the unsteady separating flow of an incompressible fluid. In particular, attention is restricted to the study of two-dimensional motion. The governing equations are derived in chapter 2. It is assumed that the incoming boundary layer has undergone a smooth separation and that the region of concern is sufficiently far downstream that viscous effects are confined to a thin free shear-layer and a thin wall-layer. A high-frequency analysis is pursued, with the relative scalings maintaining the standard triple-deck structure. The linear instability of these governing equations is readily verified and the work goes on to consider nonlinear properties. In chapter 3 the link between the current and a more global type of separation is highlighted. The study addresses the phenomenon of a finite-time break-up of the governing equations and investigates the existence of a particular break-up known to be possible in the latter-mentioned global flow (see § §3.2-3.4 for details of this more global f1ow-configuration). However, the analysis in § §3.5-3.7 suggests that such a break-up is not possible. At this point the thesis turns to a numerical solution of the governing equations. A novel type of numerical procedure is adopted in which the numerical grid is transformed in such a way that the deployment of grid nodes should enhance the numerical accuracy. This procedure is explained in chapter 4 and tested (in chapter 5) on the solution of the one-dimensional Burgers equation. The results are found to be encouraging. This numerical treatment (in chapter 6) leads to the analysis in chapter 7 where a new distinct finite-time break-up is proposed for the current flow problem. Lastly in chapter 7, the study returns to a numerical solution of the governing equations, and different initial conditions tend to confirm this new break-up numerically. The thesis closes its main body of work in chapter 8 and notes the possibility of the application of both the new break-up form and the numerical technique to related flow problems. Finally, an appendix is included which presents work in progress on a three-dimensional vortex/wave interaction.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available