Adding streamwise streaks in the plane Poiseuille flow

Martin Hollands; Carlo Cossu

doi:10.1016/j.crme.2009.03.012

Adding streamwise streaks in the plane Poiseuille flow
[Additionner des streaks dans l'écoulement de Poiseuille plan]

Présenté par : Jean-Baptiste Leblond

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

Comptes Rendus. Mécanique, Volume 337 (2009) no. 3, pp. 179-183.

Résumé
Abstract

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.

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.

Reçu le : 2009-01-08
Accepté le : 2009-03-25
Publié le : 2009-03-01

DOI : 10.1016/j.crme.2009.03.012

Keywords: Fluid mechanics, Streaks, Control
Mots-clés : Mécanique des fluides, Streaks, Contrôle d'écoulements

Affiliations des auteurs :

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

@article{CRMECA_2009__337_3_179_0,
     author = {Martin Hollands and Carlo Cossu},
     title = {Adding streamwise streaks in the plane {Poiseuille} flow},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {179--183},
     publisher = {Elsevier},
     volume = {337},
     number = {3},
     year = {2009},
     doi = {10.1016/j.crme.2009.03.012},
     language = {en},
}

TY  - JOUR
AU  - Martin Hollands
AU  - Carlo Cossu
TI  - Adding streamwise streaks in the plane Poiseuille flow
JO  - Comptes Rendus. Mécanique
PY  - 2009
SP  - 179
EP  - 183
VL  - 337
IS  - 3
PB  - Elsevier
DO  - 10.1016/j.crme.2009.03.012
LA  - en
ID  - CRMECA_2009__337_3_179_0
ER  -

%0 Journal Article
%A Martin Hollands
%A Carlo Cossu
%T Adding streamwise streaks in the plane Poiseuille flow
%J Comptes Rendus. Mécanique
%D 2009
%P 179-183
%V 337
%N 3
%I Elsevier
%R 10.1016/j.crme.2009.03.012
%G en
%F CRMECA_2009__337_3_179_0

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/

Bibliographie
Cité par

[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

Cité par Sources :

Commentaires - Politique