Bowles, Robert Ian; (1990) Applications of nonlinear viscous-inviscid interactions in liquid layer flows and transonic boundary layer transition. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

The thesis is divided into two parts. The first is concerned with the fully developed, two-dimensional, free surface flow of a viscous, incompressible fluid over a horizontal surface and down a slope at high Reynolds number. Re. In both cases we concentrate on mechanisms for upstream influence through branching from the relevant basic flow. In the horizontal case it is found that branching can occur and, if the Froude number is sufficiently large, the solution resembles a hydraulic jump. The branching is studied computationally and analytically and the theory is used in a comparison with experiments. For the half-Poiseuille flow on a slope we consider free interactions for a range of gradients, identify when separation can occur and, in the limit of small gradient, find analytic solutions for the flow forced by simple geometries. The flow on larger slopes is addressed computationally. The second part deals with some aspects of boundary layer transition beneath a transonic free stream (Mach number, M, close to unity). Again the emphasis is on high Reynolds number theory and we concentrate on lower branch, Tollmien-Schlichting disturbances. Two unsteady interactions appropriate to transonic flow are studied. The first has M 2-1 ~ 0(Re-1/9) and is an extension of the triple deck structure when the free stream reacts unsteadily. This regime links previously studied subsonic and supersonic cases. Two-dimensional disturbances are little altered but there are new, weakly nonlinear, three-dimensional effects including enhanced growth for slightly oblique disturbances and novel triad interactions. The second has M 2-1 ~ 0(Re-1/9) and links an unsteady, nonlinear free stream, capable of containing shocks, and a quasi-steady boundary layer. The possibility of a resonance linkage between shock buffetting and boundary layer thickening is addressed, being a candidate for a bypass transition mechanism in transonic flows.

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