Influence of localised smooth steps on the instability of a boundary layer

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Title: Influence of localised smooth steps on the instability of a boundary layer
Authors: Xu, H
Lombard, J
Sherwin, S
Item Type: Journal Article
Abstract: We consider a smooth, spanwise-uniform forward facing step de ned by the Gauss error function of height 4-30% and four times the width of the local boundary layer thickness δ_99. The boundary layer flow over a smooth forward-facing stepped plate is studied with particular emphasis on stabilisation and destabilisation of the two-dimensional Tollmien- Schlichting (TS) waves and subsequently on three-dimensional disturbances at transition. The interaction between TS waves at a range of frequencies and a base flow over a single or two forward facing smooth steps is conducted by linear analysis. The results indicate that for a TS wave with a frequency F 2 [140; 160] (F=! =U21 106 where ! and U1 denote the perturbation angle frequency and freestream velocity magnitude, respectively), the amplitude of the TS wave is attenuated in the unstable regime of the neutral stability curve corresponding to a at plate boundary layer. Furthermore, it is observed that two smooth forward facing steps lead to a more acute reduction of the amplitude of the TS wave. When the height of a step is increased to more than 20% of the local boundary layer thickness for a xed width parameter, the TS wave is amplified and thereby a destabilisation e ect is introduced. Therefore, stabilisation or destabilisation effect of a smooth step is typically dependent on its shape parameters. To validate the results of the linear stability analysis, where a TS wave is damped by the forward facing smooth steps direct numerical simulation (DNS) is performed. The results of the DNS correlate favorably with the linear analysis and show that for the investigated frequency of the TS wave, the K-type transition process is altered whereas the onset of the H-type transition is delayed. The results of the DNS suggest that for the perturbation with the non-dimensional frequency parameter F = 150 and in the absence of other external perturbations, two forward facing smooth steps of height 5% and 12% of the boundary layer thickness delayed H-type transition scenario and completely suppresses it for the Ktype transition. By considering Gaussian white noise with both xed and random phase shift, it is demonstrated by DNS that transition is postponed in time and space by two forward facing smooth steps.
Issue Date: 15-Mar-2017
Date of Acceptance: 31-Jan-2017
ISSN: 1469-7645
Publisher: Cambridge University Press (CUP)
Start Page: 138
End Page: 170
Journal / Book Title: Journal of Fluid Mechanics
Volume: 817
Copyright Statement: © Cambridge University Press 2017 This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (, which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Sponsor/Funder: Engineering & Physical Science Research Council (E
Royal Academy Of Engineering
Engineering & Physical Science Research Council (E
Funder's Grant Number: EP/I037946/1
Keywords: Science & Technology
Physical Sciences
Physics, Fluids & Plasmas
boundary layer stability
transition to turbulence
Fluids & Plasmas
01 Mathematical Sciences
09 Engineering
Publication Status: Published
Appears in Collections:Faculty of Engineering

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