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  • Journal of Fluid Mechanics, Volume 664
  • December 2010, pp. 74-107

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

  • V. KITSIOS (a1) (a2), L. CORDIER (a1), J.-P. BONNET (a1), A. OOI (a2) and J. SORIA (a3)
  • DOI: http://dx.doi.org/10.1017/S0022112010003617
  • Published online: 08 October 2010
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.

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Corresponding author
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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J. C. del Álamo & J. Jimenez 2003 Spectra of the very large anisotropic scales in turbulent channels. Phys. Fluids 15 (6), L41L44.


A. Alper & J. T. C. Liu 1978 On the interactions between large-scale structure and fine-grained turbulence in a free shear flow. Part II. The development of spatial interactions in the mean. Proc. R. Soc. Lond. A 359, 497523.

E. Anderson , Z. Bai , C. H. Bischof , S. Blackford , J. W. Demmel , J. J. Dongarra , J. J. Du Croz , A. Greenbaum , S. J. Hammarling , A. McKenney & D. C. Sorensen 1999 LAPACK Users' Guide, 3rd edn.SIAM.

S. Bagheri , J. Hoepffner , P. J. Schmid & D. S. Henningson 2009 Input–output analysis and control design applied to a linear model of spatially developing flows. Appl. Mech. Rev. 62 (2), 020803 (127).

J. D. Crouch , A. Garbaruk & D. Magidov 2007 Predicting the onset of flow unsteadiness based on global instability. J. Comput. Phys. 224, 924940.





K. Kupfer , A. Bers & A. K. Ram 1987 The cusp map in the complex-frequency plane for absolute instabilities. Phys. Fluids 30 (10), 30753082.

J. T. C. Liu & L. Merkine 1976 On the interactions between large-scale structure and fine-grained turbulence in a free shear flow. Part I. The development of temporal interactions in the mean. Proc. R. Soc. Lond. A 352, 213247.

R. Mankbadi & J. T. C. Liu 1981 A study of the interactions between large-scale coherent structures and fine-grained turbulence in a round jet. Phil. Trans. R. Soc. Lond. A 298 (1443), 541602.

R. Mankbadi & J. T. C. Liu 1984 Sound generated aerodynamically revisited: large-scale structures in a turbulent jet as a source of sound. Phil. Trans. R. Soc. Lond. A 311 (1516), 183217.




G. Pujals , M. García-Villalba , C. Cossu & S. Depardon 2009 A note on transient growth in turbulent channel flows. Phys. Fluids 21, 015109 (16).


S. C. Reddy , P. J. Schmid & D. S. Henningson 1993 Pseudospectra of the Orr–Sommerfeld operator. SIAM J. Appl. Maths 53 (1), 1547.



P. J. Schmid & D. S. Henningson 2001 Stability and Transition in Shear Flows. Springer.

H. B. Squire 1933 On the stability of three-dimensional disturbances of viscous fluid flow between parallel walls. Proc. R. Soc. Lond. A 142, 621628.

A. Tumin 2003 Multimode decomposition of spatially growing perturbations in a two-dimensional boundary layer. Phys. Fluids 15 (9), 25252540.

A. Tumin , M. Amitay , J. Cohen & M. D. Zhou 1996 A normal multimode decomposition method for stability experiments. Phys. Fluids 8 (10), 27772779.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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