Comptes Rendus
Adding streamwise streaks in the plane Poiseuille flow
Comptes Rendus. Mécanique, Volume 337 (2009) no. 3, pp. 179-183.

In recent investigations, finite amplitude streamwise streaks, generated with roughness elements, have been used to delay transition to turbulence. The maximum height of these roughness elements is limited by the appearance of instabilities in their near wake, therefore putting a limit on the maximum streak amplitude they can produce. Here we prove that large amplitude streaks can be generated by ‘adding’ lower amplitude streaks with multiple arrays of roughness elements.

Dans des études récentes, des streamwise streaks, engendrés avec des éléments de rugosité, ont été utilisés pour retarder la transition à la turbulence. La hauteur maximale de ces éléments de rugosité est limitée par l'apparition d'instabilité dans leur sillage proche, ce qui limite l'amplitude maximale des streaks qu'ils peuvent produire. Ici nous montrons que des streaks de grande amplitude peuvent être engendrés en « additionnant » des streaks d'amplitude inférieure par l'utilisation de lignes multiples d'éléments de rugosité.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2009.03.012
Keywords: Fluid mechanics, Streaks, Control
Mot clés : Mécanique des fluides, Streaks, Contrôle d'écoulements

Martin Hollands 1; Carlo Cossu 2

1 École polytechnique, 91128 Palaiseau cedex, France
2 Laboratoire d'hydrodynamique (LadHyX), CNRS-École polytechnique, 91128 Palaiseau cedex, France
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Martin Hollands; Carlo Cossu. Adding streamwise streaks in the plane Poiseuille flow. Comptes Rendus. Mécanique, Volume 337 (2009) no. 3, pp. 179-183. doi : 10.1016/j.crme.2009.03.012. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2009.03.012/

[1] H.K. Moffatt The interaction of turbulence with strong wind shear (A.M. Yaglom; V.I. Tatarsky, eds.), Proc. URSI–IUGG Coloq. on Atoms. Turbulence and Radio Wave Propag., Nauka, Moscow, 1967, pp. 139-154

[2] T. Ellingsen; E. Palm Stability of linear flow, Phys. Fluids, Volume 18 (1975), p. 487

[3] M.T. Landahl A note on an algebraic instability of inviscid parallel shear flows, J. Fluid Mech., Volume 98 (1980), p. 243

[4] P.J. Schmid; D.S. Henningson Stability and Transition in Shear Flows, Springer, New York, 2001

[5] C. Cossu; L. Brandt Stabilization of Tollmien–Schlichting waves by finite amplitude optimal streaks in the Blasius boundary layer, Phys. Fluids, Volume 14 (2002), p. L57-L60

[6] C. Cossu; L. Brandt On Tollmien–Schlichting waves in streaky boundary layers, Eur. J. Mech./B Fluids, Volume 23 (2004), pp. 815-833

[7] J. Fransson; L. Brandt; A. Talamelli; C. Cossu Experimental and theoretical investigation of the non-modal growth of steady streaks in a flat plate boundary layer, Phys. Fluids, Volume 16 (2004), pp. 3627-3638

[8] J. Fransson; L. Brandt; A. Talamelli; C. Cossu Experimental study of the stabilization of Tollmien–Schlichting waves by finite amplitude streaks, Phys. Fluids, Volume 17 (2005), p. 054110

[9] J. Fransson; A. Talamelli; L. Brandt; C. Cossu Delaying transition to turbulence by a passive mechanism, Phys. Rev. Lett., Volume 96 (2006), p. 064501

[10] L.H. Gustavsson Energy growth of three-dimensional disturbances in plane Poiseuille flow, J. Fluid Mech., Volume 224 (1991), pp. 241-260

[11] K.M. Butler; B.F. Farrell Three-dimensional optimal perturbations in viscous shear flow, Phys. Fluids A, Volume 4 (1992), pp. 1637-1650

[12] P. Andersson; L. Brandt; A. Bottaro; D. Henningson On the breakdown of boundary layers streaks, J. Fluid Mech., Volume 428 (2001), pp. 29-60

[13] A.W. Lang; P. Motta; P. Hidalgo; M. Westcott Bristled shark skin: a microgeometry for boundary layer control?, Bioinspiration Biomimetics, Volume 3 (2008), p. 046005

[14] A. Lundbladh, D.S. Henningson, A.V. Johansson, An efficient spectral integration method for the solution of the Navier–Stokes equations, Technical report, FFA, the Aeronautical Research Institute of Sweden, 1992

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