Journal of Fluid Mechanics


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

V. KITSIOSa1a2 c1, L. CORDIERa1, J.-P. BONNETa1, A. OOIa2 and J. SORIAa3

a1 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

a2 Walter Bassett Aerodynamics Laboratory, Department of Mechanical Engineering, University of Melbourne, Parkville 3010, Australia

a3 Laboratory For Turbulence Research in Aerospace and Combustion, Department of Mechanical and Aerospace Engineering, Monash University, Clayton 3800, Australia


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.

(Received November 05 2009)

(Revised July 05 2010)

(Accepted July 05 2010)

(Online publication October 08 2010)

Key words:

  • boundary layer stability;
  • instability;
  • turbulent boundary layers


c1 Present address: Centre for Australian Weather and Climate Research, CSIRO Marine and Atmospheric Research, Aspendale 3195, Australia. Email address for correspondence: