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Development of a nonlinear eddy-viscosity closure for the triple-decomposition stability analysis of a turbulent channel

Published online by Cambridge University Press:  08 October 2010

V. KITSIOS ,
L. CORDIER ,
J.-P. BONNET ,
A. OOI  and
J. SORIA
V. KITSIOS*
Affiliation:
Institut PPRIME, CNRS – Université de Poitiers – ENSMA, UPR 3346, ref Département Fluides, Thermique, Combustion, CEAT, 43 rue de l'Aérodrome, F-86036 Poitiers Cedex, France Walter Bassett Aerodynamics Laboratory, Department of Mechanical Engineering, University of Melbourne, Parkville 3010, Australia
L. CORDIER
Affiliation:
Institut PPRIME, CNRS – Université de Poitiers – ENSMA, UPR 3346, ref Département Fluides, Thermique, Combustion, CEAT, 43 rue de l'Aérodrome, F-86036 Poitiers Cedex, France
J.-P. BONNET
Affiliation:
Institut PPRIME, CNRS – Université de Poitiers – ENSMA, UPR 3346, ref Département Fluides, Thermique, Combustion, CEAT, 43 rue de l'Aérodrome, F-86036 Poitiers Cedex, France
A. OOI
Affiliation:
Walter Bassett Aerodynamics Laboratory, Department of Mechanical Engineering, University of Melbourne, Parkville 3010, Australia
J. SORIA
Affiliation:
Laboratory For Turbulence Research in Aerospace and Combustion, Department of Mechanical and Aerospace Engineering, Monash University, Clayton 3800, Australia
*
†Present address: Centre for Australian Weather and Climate Research, CSIRO Marine and Atmospheric Research, Aspendale 3195, Australia. Email address for correspondence: vassili.kitsios@gmail.com
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Abstract

The analysis of the instabilities in an unsteady turbulent flow is undertaken using a triple decomposition to distinguish between the time-averaged field, a coherent wave and the remaining turbulent scales of motion. The stability properties of the coherent scale are of interest. Previous studies have relied on prescribed constants to close the equations governing the evolution of the coherent wave. Here we propose an approach where the model constants are determined only from the statistical measures of the unperturbed velocity field. Specifically, a nonlinear eddy-viscosity model is used to close the equations, and is a generalisation of earlier linear eddy-viscosity closures. Unlike previous models the proposed approach does not assume the same dissipation rate for the time- and phase-averaged fields. The proposed approach is applied to a previously published turbulent channel flow, which was harmonically perturbed by two vibrating ribbons located near the channel walls. The response of the flow was recorded at several downstream stations by phase averaging the probe measurements at the same frequency as the forcing. The experimentally measured growth rates and velocity profiles, are compared to the eigenvalues and eigenvectors resulting from the stability analysis undertaken herein. The modes recovered from the solution of the eigenvalue problem, using the nonlinear eddy-viscosity model, are shown to capture the experimentally measured spatial decay rates and mode shapes of the coherent scale.

JFM classification

Boundary Layers: Boundary layer stability Instability: Instability Turbulent Flows: Turbulent boundary layers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 664 , 10 December 2010 , pp. 74 - 107
Copyright
Copyright © Cambridge University Press 2010

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