Imperial College London
Professor Xuesong Wu

ProfessorXuesongWu

Faculty of Natural Sciences, Department of Mathematics

Professor of Applied Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 8494x.wu Website

 
 
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Location

 

738Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Wu:2016:10.1017/jfm.2016.125,
author = {Wu, X and Dong, M},
doi = {10.1017/jfm.2016.125},
journal = {Journal of Fluid Mechanics},
pages = {68--108},
title = {A local scattering theory for the effects of isolated roughness on boundary-layer instability and transition: transmission coefficient as an eigenvalue},
url = {http://dx.doi.org/10.1017/jfm.2016.125},
volume = {794},
year = {2016}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - This paper is concerned with the rather broad issue of the impact of abrupt changes (such as isolated roughness, gaps and local suctions) on boundary-layer transition. To fix the idea, we consider the influence of a two-dimensional localized hump (or indentation) on an oncoming Tollmien-Schlichting (T-S) wave. We show that when the length scale of the former is comparable with the characteristic wavelength of the latter, the key physical mechanism to affect transition is through scattering of T-S waves by the roughness-induced mean-flow distortion. An appropriate mathematical theory, consisting of the boundary-value problem governing the local scattering,is formulated based on triple deck formalism. The transmission co efficient, defined as the ratio of the amplitude of the T-S wave downstream the roughnessto that upstream, serves to characterize the impact on transition. The transmission coefficient appears as the eigenvalue of the discretized boundary-value problem. The latter is solved numerically, and the dependenceof the eigenvalue on the height and width of the roughness and the frequencyof the T-S wave is investigated. For a roughness element without causing separation, the transmission coefficient is found to be about 1:5 for typical frequencies, indicating a moderate but appreciable destabilizing effect. For a roughness causing incipient separation, the transmission coefficient can be as large as O(10), suggesting that immediate transition may take place at the roughness site. A roughness element with a fixed height produces the strongest impact when its width is comparable with the T-S wavelength, in which case the traditional linear stability theory is in valid. The latter how ever holds approximately when the roughness width is sufficiently large. By studying the two-hump case, a criterion when two roughness elements can be regarded as being isolated is suggested. The transmission coefficient can be converted to an equivalent N-factor increment, by makin
AU  - Wu,X
AU  - Dong,M
DO  - 10.1017/jfm.2016.125
EP  - 108
PY  - 2016///
SN  - 0022-1120
SP  - 68
TI  - A local scattering theory for the effects of isolated roughness on boundary-layer instability and transition: transmission coefficient as an eigenvalue
T2  - Journal of Fluid Mechanics
UR  - http://dx.doi.org/10.1017/jfm.2016.125
UR  - http://hdl.handle.net/10044/1/30273
VL  - 794
ER  -
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