Vickers, Ian Paul; (1993) Nonlinear effects in two-dimensional separating-flow transition. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

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.

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