Boundary-layer effects in liquid-layer flows
In this thesis we describe various regimes of practical and theoretical significance that arise in the laminar two-dimensional flow of a layer of an incompressible viscous fluid over a solid surface at high Reynolds number. In Part I we consider steady flows over a distorted rigid surface. Almost uniform flows are considered first, when the distortion is sufficient to provoke a viscous-inviscid interaction, and therefore boundary-layer separation. The two cases of supercritical and subcritical flow have quite distinct features, and are discussed separately. The governing equations in each case require a numerical treatment in general, but analytical progress has been made in certain important regimes e. g. when the distortion is relatively small and linearisation of the problem is possible. Next, the grossly separated motion of fully-developed flows over large obstacles, with dimensions of the order of the depth of the liquid layer, is studied on the basis of inviscid Kirchhoff free-streamline theory. Some comparisons of the theory with recent experiments are also given. In Part II we discuss unsteady and instability aspects of two-dimensional flow over a flat surface. It is shown that viscous and mean flow effects can combine to give instability in some cases, whereas previous studies have only found viscous effects to be stabilising. Unsteadiness of a two-layer fluid flow, with fluids of different viscosity and density, and incorporating surface tension effects, is also discussed. In Part III, deviating from the above theme slightly, we discuss briefly the steady, high-Reynolds-number flow in an asymmetric branching channel, again in the context of viscous-inviscid interactions. The asymmetry is found to force a large-scale response both up- and downstream of the start of the bifurcation. The aim is to find the pressure distributions on the channel walls and on the dividing body. This requires the use of a Wiener-Hopf technique in view of the mixed boundary conditions.