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Instability of streaks in wall turbulence with adverse pressure gradient

Published online by Cambridge University Press:  02 June 2011

MATTHIEU MARQUILLIE ,
UWE EHRENSTEIN  and
JEAN-PHILIPPE LAVAL
MATTHIEU MARQUILLIE
Affiliation:
CNRS, UMR 8107, F-59650 Villeneuve d'Ascq, France Université Lille Nord de France, F-59000 Lille, France
UWE EHRENSTEIN*
Affiliation:
IRPHÉ UMR 6594, Aix-Marseille Université, CNRS, F-13384 Marseille, France
JEAN-PHILIPPE LAVAL
Affiliation:
CNRS, UMR 8107, F-59650 Villeneuve d'Ascq, France Université Lille Nord de France, F-59000 Lille, France
*
†Email address for correspondence: ehrenstein@irphe.univ-mrs.fr
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Abstract

A direct numerical simulation of a turbulent channel flow with a lower curved wall is performed at Reynolds number Reτ ≈ 600. Low-speed streak structures are extracted from the turbulent flow field using methods known as skeletonization in image processing. Individual streaks in the wall-normal plane averaged in time and superimposed to the mean streamwise velocity profile are used as basic states for a linear stability analysis. Instability modes are computed at positions along the lower and upper wall and the instability onset is shown to coincide with the strong production peaks of turbulent kinetic energy near the maximum of pressure gradient on both the curved and the flat walls. The instability modes are spanwise-symmetric (varicose) for the adverse pressure gradient streak base flows with wall-normal inflection points, when the total average of the detected streaks is considered. The size and shape of the counter-rotating streamwise vortices associated with the instability modes are shown to be reminiscent of the coherent vortices emerging from the streak skeletons in the direct numerical simulation. Conditional averages of streaks have also been computed and the distance of the streak's centre from the wall is shown to be an essential parameter. For the upper-wall weak pressure gradient flow, spanwise-antisymmetric (sinuous) instability modes become unstable when sets of highest streaks are considered, whereas varicose modes dominate for the streaks closest to the wall.

JFM classification

Instability: Instability Turbulent Flows: Turbulent boundary layers

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Type
Papers
Information
Journal of Fluid Mechanics , Volume 681 , 25 August 2011 , pp. 205 - 240
Copyright
Copyright © Cambridge University Press 2011

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References

REFERENCES

Acarlar, M. S. & Smith, C. R. 1987 A study of hairpin vortices in a laminar boundary layer. Part 2. Hairpin vortices generated by fluid injection. J. Fluid Mech. 175, 43–83.Google Scholar
del Álamo, J. C. & Jiménez, J. 2003 Spectra of the very large anisotropic scales in turbulent channels. Phys. Fluids 15 (6), L41–L44.CrossRefGoogle Scholar
del Álamo, J. C. & Jiménez, J. 2006 Linear energy amplification in turbulent channels. J. Fluid Mech. 559, 205–213.CrossRefGoogle Scholar
del Álamo, J. C., Jiménez, J., Zandonade, P. & Moser, R. D. 2004 Scaling of the energy spectra of turbulent channels. J. Fluid Mech. 500, 135–144.CrossRefGoogle Scholar
Andersson, P., Brandt, L., Henningsson, D. S. & Bottaro, A. 2001 On the breakdown of boundary layer streaks. J. Fluid Mech. 428, 29–60.CrossRefGoogle Scholar
Asai, M., Konishi, Y., Oizumi, Y. & Nishika, M. 2007 Growth and breakdown of low-speed streaks leading to wall turbulence. J. Fluid Mech. 586, 371–396.CrossRefGoogle Scholar
Asai, M., Manigawa, M. & Nishioka, M. 2002 The instability and breakdown of near wall low-speed streaks. J. Fluid Mech. 455, 289–314.CrossRefGoogle Scholar
Aubertine, C. D. & Eaton, J. K. 2006 Reynolds number scaling in a non-equilibrium turbulent boundary layer with mild adverse pressure gradient. Intl J. Heat Fluid Flow 27, 566–575.CrossRefGoogle Scholar
Bernard, A., Foucaut, J. M., Dupont, P. & Stanislas, M. 2003 Decelerating boundary layer : a new scaling and mixing length model. AIAA J. 41 (2), 248–255.Google Scholar
Brandt, L. 2007 Numerical studies of the instability and breakdown of a boundary-layer low-speed streak. Eur. J. Mech. (B/Fluids) 26, 64–82.CrossRefGoogle Scholar
Brandt, L., Cossu, C., Chomaz, J.-M., Huerre, P. & Henningson, D. S. 2003 On the convectively unstable nature of optimal streaks in boundary layers. J. Fluid Mech. 485, 221–242.CrossRefGoogle Scholar
Brandt, L. & Henningson, D. S. 2002 Transition of streamwise streaks in zero-pressure-gradient boundary layers. J. Fluid Mech. 472, 229–261.CrossRefGoogle Scholar
Brandt, L. & de Lange, H. C. 2008 Streak interactions and breakdown in boundary layer flows. Phys. Fluids 20, 024107.CrossRefGoogle Scholar
Brandt, L., Schlatter, P. & Henningson, D. S. 2004 Transition in boundary layers subject to free-stream turbulence. J. Fluid Mech. 517, 167–198.CrossRefGoogle Scholar
Castillo, L. & George, W. K. 2001 Similarity analysis for turbulent boundary layers with pressure gradient: Outer flow. AIAA J. 39, 41–47.CrossRefGoogle Scholar
Clauser, F. H. 1954 Turbulent boundary layers in adverse pressure gradients. J. Aero. Sci. 21 (2), 91–108.CrossRefGoogle Scholar
Cornea, N. D., Silver, D. & Min, P. 2007 Curve-skeleton properties, applications, and algorithms. IEEE Trans. Vis. Comput. Graphics 13 (3), 530–548.CrossRefGoogle ScholarPubMed
Cossu, C., Pujals, G. & Depardon, S. 2009 Optimal transient growth and very large-scale structures in turbulent boundary layers. J. Fluid Mech. 619, 79–94.CrossRefGoogle Scholar
Elofsson, P. A., Kawakami, M. & Alfredsson, P. H. 1999 Experiments on the stability of streamwise streaks in plane Poiseuille flow. Phys. Fluids 11, 915–930.CrossRefGoogle Scholar
Gallaire, F., Marquillie, M. & Ehrenstein, U. 2007 Three-dimensional transverse instabilities in detached boundary layers. J. Fluid Mech. 571, 221–233.CrossRefGoogle Scholar
Gonzales, R. & Woods, R. 2008 Digital Image Processing, 3rd edn. Upper Saddle River, NJ: Prentice Hall.Google Scholar
Hall, P. & Horseman, N. J. 1991 The linear inviscid secondary instability of longitudinal vortex structures in boundary layers. J. Fluid Mech. 232, 357–375.CrossRefGoogle Scholar
Hoepffner, J., Brandt, L. & Henningson, D. S. 2005 Transient growth on boundary layer streaks. J. Fluid Mech. 537, 91–100.CrossRefGoogle Scholar
Jiménez, J. & Moin, P. 1991 The minimal flow unit in near wall turbulence. J. Fluid Mech. 225, 221–240.Google Scholar
Jiménez, J. & Pinelli, A. 1999 The autonomous cycle of near wall turbulence. J. Fluid Mech. 389, 335–359.Google Scholar
Kawahara, G., Jiménez, J., Uhlmann, M. & Pinelli, A. 1998 The instability of streaks in near-wall turbulence. Annual Research Brief, Center for Turbulence Research, p. 155.Google Scholar
Laval, J.-P. & Marquillie, M. 2009 Direct numerical simulations of converging–diverging channel flow. In Progress in Wall Turbulence: Understanding and Modelling (ed. Stanislas, M., Jimenez, J. & Marusic, I., pp. 203–210, April 21–23. Springer.Google Scholar
Lee, J.-H. & Sung, H. J. 2008 Effects of an adverse pressure gradient on a turbulent boundary layer. Intl J. Heat Fluid Flow 29, 568–578.Google Scholar
Lee, J.-H. & Sung, H. J. 2009 Large scale structure of turbulent boundary layer subjected to an adverse pressure gradient. In 6th International Symposium on Turbulence and Shear Flow Phenomena, pp. 153–158. Seoul, Korea, 22–24 June, 2009.Google Scholar
Lin, J., Laval, J.-P., Foucaut, J.-M. & Stanislas, M. 2008 Quantitative characterization of coherent structures in the buffer layer of near-wall turbulence. Part 1: Streaks. Exp. Fluids 45 (6), 999–1013.CrossRefGoogle Scholar
Mans, J., de Lange, H. C. & van Steenhoven, A. A. 2007 Sinous breakdown in a flat plate boundary layer exposed to free-stream turbulence. Phys. Fluids 19, 088101.Google Scholar
Marquillie, M., Laval, J.-P. & Dolganov, R. 2008 Direct numerical simulation of separated channel flows with a smooth profile. J. Turbulence 9 (1), 1–23.CrossRefGoogle Scholar
Na, Y. & Moin, P. 1998 Direct numerical simulation of a separated turbulent boundary layer. J. Fluid Mech. 374, 379–405.CrossRefGoogle Scholar
Nayar, O. & Ortega, U. 1993 Computation of selected eigenvalues of generalized eigenvalue problems. J. Comput. Phys. 108, 8–14.CrossRefGoogle Scholar
Palágyi, K. & Kuba, A. 1999 A parallel 3D 12-subiteration thinning algorithm. Graph. Models Image Process. 61, 199–221.CrossRefGoogle Scholar
Palágyi, K., Tschirren, J., Hoffman, E. A. & Sonka, M. 2006 Quantitative analysis of pulmonary airway tree structures. Comput. Biol. Med. 36, 974–996.Google Scholar
Park, J., Hwang, Y. & Cossu, C. 2011 On the stability of large-scale streaks in turbulent Couette and Poiseuille flows. C. R. Mécanique 339, 1–5.CrossRefGoogle Scholar
Reddy, S. C., Schmid, P. J., Baggett, J. S. & Henningson, D. S. 1998 On the stability of streamwise streaks and transition thresholds in plane channel flow. J. Fluid Mech. 455, 269–303.CrossRefGoogle Scholar
Reynolds, W. C. & Hussain, A. K. M. F. 1972 The mechanics of an organized wave in turbulent shear flow. Part 3. Theoretical models and comparison with experiments. J. Fluid Mech. 54, 263–288.CrossRefGoogle Scholar
Schlatter, P., Brandt, L., de Lange, H. C. & Henningson, D. S. 2008 On streak breakdown in bypass transition. Phys. Fluids 20, 101505.Google Scholar
Schmid, P. J. & Henningson, D. S. 2001 Stability and Transition in Shear Flows. Springer.CrossRefGoogle Scholar
Schoppa, W. & Hussain, F. 2002 Coherent structure generation in near wall turbulence. J. Fluid. Mech. 453, 57–108.CrossRefGoogle Scholar
Schoppa, W., Hussain, F. & Metcalfe, R. W. 1995 A new mechanism of small-scale transition in a plane mixing layer: core dynamics of spanwise vortices. J. Fluid Mech. 298, 23–80.CrossRefGoogle Scholar
Shah, S. I., Stanislas, M. & Laval, J.-P. 2010 A specific behavior of adverse pressure gradient near wall flows. In Progress in Wall Turbulence: Understanding and Modelling (ed. Stanislas, M., Jimenez, J. & Marusic, I.), pp. 257–265., April 21-23. Springer.Google Scholar
Simpson, R. L. 1981 A review of some phenomena in turbulent flow separation. Trans. ASME: J. Fluids Engng 103, 520–533.Google Scholar
Skåre, P. E. & Krogstad, P.-Å 1994 A turbulent boundary layer near separation. J. Fluid Mech. 272, 319–348.CrossRefGoogle Scholar
Skote, M., Haritonidis, J. H. & Henningson, D. S. 2002 Varicose instabilities in turbulent boundary layers. Phys. Fluids 14 (7), 2309–2323.CrossRefGoogle Scholar
Skote, M. & Henningson, D. S. 2002 Direct numerical simulation of separating turbulent boundary layers. J. Fluid Mech. 471, 107–136.CrossRefGoogle Scholar
Song, S. & Eaton, J. K. 2004 Reynolds number effects on a turbulent boundary layer with separation, reattachment, and recovery. Exp. Fluids 36, 246–258.CrossRefGoogle Scholar
Spalart, P. R. & Watmuff, J. H. 1993 Experimental and numerical investigation of a turbulent boundary layer with pressure gradients. J. Fluid Mech. 249, 337–371.Google Scholar
Waleffe, F. 1997 On a self-sustaining process in shear flows. Phys. Fluids 9, 883–900.CrossRefGoogle Scholar
Wilcox, D. C. 1993 Turbulence Modeling for CFD. DCW Industries, Inc.Google Scholar