On the stability of large-scale streaks in turbulent Couette and Poiseulle flows

Junho Park; Yongyun Hwang; Carlo Cossu

doi:10.1016/j.crme.2010.10.012

On the stability of large-scale streaks in turbulent Couette and Poiseulle flows
[Sur la stabilité des streaks à grande échelle dans les écoulements de Couette et Poiseuille turbulents]

Junho Park ¹ ; Yongyun Hwang ¹ ; Carlo Cossu ^2,³

¹ Laboratoire d'hydrodynamique (LadHyX), École polytechnique, 91128 Palaiseau cedex, France
² CNRS – Institut de mécanique des fluides de Toulouse (IMFT), allée du Pr. Camille-Soula, 31400 Toulouse, France
³ Département de mécanique, École polytechnique, 91128 Palaiseau cedex, France

Comptes Rendus. Mécanique, Volume 339 (2011) no. 1, pp. 1-5.

Résumé
Abstract

L'instabilité linéaire secondaire des streaks à grande échelle est étudiée dans les écoulements de Couette turbulent à ${Re}_{τ} = 52$ et Poiseuille turbulent à ${Re}_{τ} = 300$ . Les streaks sont calculés en résolvant les équations de Navier–Stokes moyennées selon Reynolds en utilisant un modèle de viscosité turbulente. Les conditions initiales optimales, induisant la plus grande croissance transitoire, sont utilisées ; quand l'amplitude des tourbillons optimaux initiaux est augmentée, l'amplitude des streaks augmente aussi. Les streaks deviennent instables quand leur amplitude est supérieure à environ $18 %$ de la différence de vitesse entre les deux parois dans l'écoulement de Couette turbulent et $21 %$ de la vitesse au centre du canal dans l'écoulement de Poiseuille turbulent. Quand l'amplitude des streaks est suffisamment élevée les instabilités atteignent des taux d'amplification significatifs dans une bande de longueurs d'onde qui est en bon accord avec les longueurs d'onde typiques observées dans les région externe.

The linear secondary stability of large-scale optimal streaks in turbulent Couette flow at ${Re}_{τ} = 52$ and Poiseulle flow at ${Re}_{τ} = 300$ is investigated. The streaks are computed by solving the nonlinear two-dimensional Reynolds-averaged Navier–Stokes equations using an eddy-viscosity model. Optimal initial conditions leading the largest linear transient growth are used, and as the amplitude of the initial vortices increases, the amplitude of streaks gradually increases. Instabilities of the streaks appear when their amplitude exceeds approximately $18 %$ of the velocity difference between walls in turbulent Couette flow and $21 %$ of the centerline velocity in turbulent Poiseuille flow. When the amplitude of the streaks is sufficiently large, the instabilities attain significant growth rates in a finite range of streamwise wavenumbers that shows good agreement with the typical streamwise wavenumbers of the large-scale motions in the outer region.

Reçu le : 2010-06-17
Accepté le : 2010-10-29
Publié le : 2010-12-17

DOI : 10.1016/j.crme.2010.10.012

Keywords: Instability, Secondary instability, Large-scale streaks, Turbulent flow
Mot clés : Instabilité, Instabilité secondaire, Streaks à grande échelle, Écoulements turbulent

Affiliations des auteurs :

Junho Park ¹ ; Yongyun Hwang ¹ ; Carlo Cossu ^{2, 3}

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     author = {Junho Park and Yongyun Hwang and Carlo Cossu},
     title = {On the stability of large-scale streaks in turbulent {Couette} and {Poiseulle} flows},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {1--5},
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     language = {en},
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Junho Park; Yongyun Hwang; Carlo Cossu. On the stability of large-scale streaks in turbulent Couette and Poiseulle flows. Comptes Rendus. Mécanique, Volume 339 (2011) no. 1, pp. 1-5. doi : 10.1016/j.crme.2010.10.012. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2010.10.012/

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