Effects of distributed roughness on crossflow instability through generalized resonance mechanisms

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Title: Effects of distributed roughness on crossflow instability through generalized resonance mechanisms
Authors: He, J
Butler, A
Wu, X
Item Type: Journal Article
Abstract: Experiments have shown that micron-sized distributed surface roughness can significantly promote transition in a three-dimensional boundary layer dominated by crossflow instability. This sensitive effect has not yet been fully explained physically and mathematically. Past studies focused on surface roughness exciting crossflow vortices and/or changing the local stability characteristics. The present paper seeks possible additional mechanisms by investigating the effects of distributed surface roughness on crossflow instability through resonant interactions with eigenmodes. A key observation is that the perturbation induced by roughness with specific wavenumbers can interact with two eigenmodes (travelling and stationary vortices) through triadic resonance, or interact with one eigenmode (stationary vortices) through Bragg scattering. Unlike the usual triadic resonance of neutral, or nearly neutral, eigenmodes, the present triadic resonance can take place among modes with growth rates, provided that these are equal; unlike the usual Bragg scattering involving neutral waves, crossflow stationary vortices can also be unstable. For these amplifying waves, the generalized triadic resonance and Bragg scattering are put forward, and the resulting corrections to the growth rates are derived by a multiple-scale method. The analysis is extended to the case where up to four crossflow vortices interact with each other in the presence of suitable roughness components. The numerical results for Falkner–Skan–Cooke boundary layers show that roughness with a small height (a few percent of the local boundary-layer thickness) can change growth rates substantially (by a more-or-less amount). This sensitive effect is attributed to two facts: (i) the resonant nature of the triadic interaction and Bragg scattering, which makes the correction to the growth rate proportional to the roughness height, and (ii) the wavenumbers of the roughness component required for the resonance are close to those of the neutral stationary crossflow modes, as a result of which a small roughness can generate a large response. Another important effect of roughness is that its presence renders the participating eigenmodes, which are otherwise independent, fully coupled. Our theoretical results suggest that micron-sized distributed surface roughness influences significantly both the amplification and spectral composition of crossflow vortices.
Issue Date: 10-Jan-2019
Date of Acceptance: 6-Oct-2018
ISSN: 0022-1120
Publisher: Cambridge University Press (CUP)
Start Page: 787
End Page: 831
Journal / Book Title: Journal of Fluid Mechanics
Volume: 858
Copyright Statement: © 2018 Cambridge University Press. This paper has been accepted for publication and will appear in a revised form, subsequent to peer-review and/or editorial input by Cambridge University Press.
Sponsor/Funder: Engineering & Physical Science Research Council (E
Funder's Grant Number: EP/I037946/1
Keywords: 01 Mathematical Sciences
09 Engineering
Fluids & Plasmas
Publication Status: Published
Online Publication Date: 2018-11-12
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences

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