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The laminar generalized Stokes layer and turbulent drag reduction

Published online by Cambridge University Press:  16 November 2010

MAURIZIO QUADRIO  and
PIERRE RICCO
MAURIZIO QUADRIO*
Affiliation:
Dipartimento di Ingegneria Aerospaziale, Politecnico di Milano, via La Masa 34, 20156 Milano, Italy
PIERRE RICCO
Affiliation:
Department of Mechanical Engineering, King's College London, Strand, London WC2R 2LS, UK
*
†Email address for correspondence: [email protected]
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Abstract

This paper considers plane channel flow modified by waves of spanwise velocity applied at the wall and travelling along the streamwise direction. Both laminar and turbulent regimes for the streamwise flow are studied. When the streamwise flow is laminar, it is unaffected by the spanwise flow induced by the waves. This flow is a thin, unsteady and streamwise-modulated boundary layer that can be expressed in terms of the Airy function of the first kind. We name it the generalized Stokes layer because it reduces to the classical oscillating Stokes layer in the limit of infinite wave speed. When the streamwise flow is turbulent, the laminar generalized Stokes layer solution describes well the space-averaged turbulent spanwise flow, provided that the phase speed of the waves is sufficiently different from the turbulent convection velocity, and that the time scale of the forcing is smaller than the life time of the near-wall turbulent structures. Under these conditions, the drag reduction is found to scale with the Stokes layer thickness, which renders the laminar solution instrumental for the analysis of the turbulent flow. A classification of the turbulent flow regimes induced by the waves is presented by comparing parameters related to the forcing conditions with the space and time scales of the turbulent flow.

JFM classification

Flow Control: Drag reduction Turbulent Flows: Turbulence control
Type
Papers
Information
Journal of Fluid Mechanics , Volume 667 , 25 January 2011 , pp. 135 - 157
Copyright
Copyright © Cambridge University Press 2010

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