Brown, Philippa Gail; (1994) High Reynolds number vortex flows: Vortex/Rayleigh wave interaction and the compressible leading-edge vortex. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

The work undertaken in this thesis falls into two parts. The term 'vortex' is applicable to each, although rather in a different context. In Part I we discuss the stability of a laminar boundary layer to inviscid Rayleigh perturbations of such an amplitude and on such a streamwise length scale that the mean flow (the vortex) develops along with the perturbations (the wave). This phenomenon is termed vortex/wave interaction and the relevant equations (Hall and Smith 1991) have already appeared in the literature. In Chapter 1 of Part I we present a solution valid in the neighbourhood of the neutral point where the non-linear interaction is initiated. This theory is illustrated by a representative boundary-layer profile and confirms the viability of the proposed structure. In Chapter 2 the same physical situation is examined but on a streamwise length scale that is, in terms of the Reynolds number R that is asymptotically large, even shorter. On this new length scale the Hall-Smith interaction equations do not apply, and the resulting amplitude satisfies an integro-differential equation. This is solved completely and is shown to possess solutions in addition to the one that matches downstream onto the algebraic solution of Chapter 1. It is expected that the periodic self-persisting solutions found here may have relevance to laminar turbulent transition. The problem considered in Part II concerns a vortex in a more conventional sense, namely a leading-edge vortex that separates from a delta wing at incidence. The solution presented describes a conical inviscid compressible vortex which is matched to an inner viscous core. The presence of this vortex above a wing generates low pressure and, as a consequence, high lift. The analogous analysis has previously been undertaken for an incompressible fluid.

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