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Amplification of coherent streaks in the turbulent Couette flow: an input–output analysis at low Reynolds number

Published online by Cambridge University Press:  05 January 2010

YONGYUN HWANG  and
CARLO COSSU
YONGYUN HWANG
Affiliation:
Laboratorie d'Hydrodynamique (LadHyX), CNRS-École Polytechnique, F-91128 Palaiseau, France
CARLO COSSU*
Affiliation:
Laboratorie d'Hydrodynamique (LadHyX), CNRS-École Polytechnique, F-91128 Palaiseau, France
*
†Email address for correspondence: [email protected]
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Abstract

We compute the optimal response of the turbulent Couette mean flow to initial conditions, harmonic and stochastic forcing at Re = 750. The equations for the coherent perturbations are linearized near the turbulent mean flow and include the associated eddy viscosity. The mean flow is found to be linearly stable but it has the potential to amplify steamwise streaks from streamwise vortices. The most amplified structures are streamwise uniform and the largest amplifications of the energy of initial conditions and of the variance of stochastic forcing are realized by large-scale streaks having spanwise wavelengths of 4.4h and 5.2h respectively. These spanwise scales compare well with the ones of the coherent large-scale streaks observed in experimental realizations and direct numerical simulations of the turbulent Couette flow. The optimal response to the harmonic forcing, related to the sensitivity to boundary conditions and artificial forcing, can be very large and is obtained with steady forcing of structures with larger spanwise wavelength (7.7h). The optimal large-scale streaks are furthermore found proportional to the mean turbulent profile in the viscous sublayer and up to the buffer layer.

JFM classification

Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 643 , 25 January 2010 , pp. 333 - 348
Copyright
Copyright © Cambridge University Press 2010

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