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Instability of streaks in wall turbulence with adverse pressure gradient

Published online by Cambridge University Press:  02 June 2011

MATTHIEU MARQUILLIE ,
UWE EHRENSTEIN  and
JEAN-PHILIPPE LAVAL
MATTHIEU MARQUILLIE
Affiliation:
CNRS, UMR 8107, F-59650 Villeneuve d'Ascq, France Université Lille Nord de France, F-59000 Lille, France
UWE EHRENSTEIN*
Affiliation:
IRPHÉ UMR 6594, Aix-Marseille Université, CNRS, F-13384 Marseille, France
JEAN-PHILIPPE LAVAL
Affiliation:
CNRS, UMR 8107, F-59650 Villeneuve d'Ascq, France Université Lille Nord de France, F-59000 Lille, France
*
†Email address for correspondence: ehrenstein@irphe.univ-mrs.fr
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Abstract

A direct numerical simulation of a turbulent channel flow with a lower curved wall is performed at Reynolds number Reτ ≈ 600. Low-speed streak structures are extracted from the turbulent flow field using methods known as skeletonization in image processing. Individual streaks in the wall-normal plane averaged in time and superimposed to the mean streamwise velocity profile are used as basic states for a linear stability analysis. Instability modes are computed at positions along the lower and upper wall and the instability onset is shown to coincide with the strong production peaks of turbulent kinetic energy near the maximum of pressure gradient on both the curved and the flat walls. The instability modes are spanwise-symmetric (varicose) for the adverse pressure gradient streak base flows with wall-normal inflection points, when the total average of the detected streaks is considered. The size and shape of the counter-rotating streamwise vortices associated with the instability modes are shown to be reminiscent of the coherent vortices emerging from the streak skeletons in the direct numerical simulation. Conditional averages of streaks have also been computed and the distance of the streak's centre from the wall is shown to be an essential parameter. For the upper-wall weak pressure gradient flow, spanwise-antisymmetric (sinuous) instability modes become unstable when sets of highest streaks are considered, whereas varicose modes dominate for the streaks closest to the wall.

JFM classification

Instability: Instability Turbulent Flows: Turbulent boundary layers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 681 , 25 August 2011 , pp. 205 - 240
Copyright
Copyright © Cambridge University Press 2011

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