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Title: Stationary vortices in three-dimensional boundary layers : non-parallelism, receptivity, and the effects of surface roughness
Author: Butler, Adam James Owen
ISNI:       0000 0004 7657 5724
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2017
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In this thesis we investigate the early development of stationary crossflow vortices in a swept-wing boundary layer. We focus in particular on the effects of non-parallelism, receptivity to surface roughness, and weakly-nonlinear resonant interaction between vortices and roughness, studying these using a large-Reynolds-number asymptotic approach. We first consider the earliest development of the crossflow vortices. We show that non-parallelism plays a leading-order role in determining the growth rate. In this regime, the instability is aligned with the local wall shear at leading order and so has a marginally-separated triple-deck structure. Stationary crossflow vortices thus have a viscous and non-parallel genesis near the leading edge. If the 'effective pressure minimum' occurs within this regime, the previous analysis must be regularised within a localised region around it. A new instability occurs. The flow maintains its three-tiered structure, but the pressure perturbation is no longer interactive between the decks. Downstream, the instability evolves into a Cowley, Hocking, & Tutty instability associated with a critical layer in the lower deck. We next consider the generation of stationary crossflow modes by surface roughness in the non-parallel regime. The flow responds differently to different Fourier spectral content of the roughness, giving the lower deck a two-part structure. We find that roughness with sharper edges generates stronger modes. Finally, we investigate weakly-nonlinear interactions between extant stationary modes and the perturbation induced by periodic roughness. These interactions modulate the eigenmode amplitudes, provided their wavenumbers satisfy certain relations, and include generalised Bragg Scattering and Triadic Resonance, as well as combinations of the two. For rather moderate roughness heights, this modulation can be significant compared to the leading-order growth rate, or even larger than it. The largest response occurs for modes near the upper branch. Through Triadic Resonance, two otherwise-independent eigenmodes become coupled, and the ratio of their amplitudes fixed.
Supervisor: Wu, Xuesong Sponsor: Engineering and Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral