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Laminar streak growth above a spanwise oscillating wall

Published online by Cambridge University Press:  06 March 2015

Peter D. Hicks  and
Pierre Ricco
Peter D. Hicks*
Affiliation:
School of Engineering, Fraser Noble Building, King’s College, University of Aberdeen, Aberdeen AB24 3UE, UK
Pierre Ricco
Affiliation:
Department of Mechanical Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK
*
†Email address for correspondence: p.hicks@abdn.ac.uk
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Abstract

The use of spanwise wall oscillations to attenuate the growth of laminar streaks within the incompressible Blasius boundary layer is investigated. As in the case of the flow above a stationary flat plate, studied by Leib et al. (J. Fluid Mech., vol. 380, 1999, pp. 169–203), free-stream convected gusts interact with the boundary layer to drive the streak growth. Spanwise wall oscillations can either reduce or increase the total energy of the laminar streaks, depending upon the wall oscillation amplitude and frequency, as well as the free-stream gust properties. Reductions in streak energies of up to 90 % are obtained, indicating that spanwise wall oscillations are an effective technique for attenuating the laminar streak growth. Therefore they may suppress secondary boundary-layer instabilities and delay transition. The laminar boundary-layer base flow matches the Blasius profile in the streamwise and wall-normal directions, while in the spanwise direction a generalized version of the classical Stokes layer profile (generated by a wall oscillating beneath a quiescent fluid) occurs, which evolves downstream due to non-parallel flow effects. Via a Wentzel–Kramers–Brillouin–Jeffreys analysis, this generalized Stokes layer is shown to approach the classical Stokes layer in the limit of large downstream distances or high-frequency plate oscillations. The laminar streaks forced by the generalized and the classical Stokes flows differ significantly, which implies that the choice of the spanwise base flow may affect the secondary instability and transition in this flow. The analysis also proves that the use of the classical Stokes layer as spanwise base flow, as employed by Hack & Zaki (Phys. Fluids. vol. 24 (3), 2012, 034101), is inappropriate.

JFM classification

Aerodynamics: Aerodynamics Boundary Layers: Boundary Layers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 768 , 10 April 2015 , pp. 348 - 374
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Copyright
© 2015 Cambridge University Press 

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