Hostname: page-component-66d9dcfd78-jd69p Total loading time: 0 Render date: 2026-08-08T03:21:39.649Z Has data issue: false hasContentIssue false
  • English
  • Français

Turbulent spots in a channel: large-scale flow and self-sustainability

Published online by Cambridge University Press:  14 August 2013

Grégoire Lemoult ,
Jean-Luc Aider  and
José Eduardo Wesfreid
Grégoire Lemoult*
Affiliation:
Laboratoire de Physique et Mécanique des Milieux Hétérogènes (PMMH), UMR CNRS 7636, ESPCI, UPMC, Paris Diderot, 10 rue Vauquelin, 75005 Paris, France
Jean-Luc Aider
Affiliation:
Laboratoire de Physique et Mécanique des Milieux Hétérogènes (PMMH), UMR CNRS 7636, ESPCI, UPMC, Paris Diderot, 10 rue Vauquelin, 75005 Paris, France
José Eduardo Wesfreid
Affiliation:
Laboratoire de Physique et Mécanique des Milieux Hétérogènes (PMMH), UMR CNRS 7636, ESPCI, UPMC, Paris Diderot, 10 rue Vauquelin, 75005 Paris, France
*
†Email address for correspondence: gregoire.lemoult@espci.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

Using a large-time-resolved particle image velocimetry field of view, a developing turbulent spot is followed in space and time in a rectangular channel flow for more than 100 advective time units. We show that the flow can be decomposed into a large-scale motion consisting of an asymmetric quadrupole centred on the spot and a small-scale part consisting of streamwise streaks. From the temporal evolution of the energy of the streamwise and spanwise velocity perturbations, it is suggested that a self-sustaining process can occur in a turbulent spot above a given Reynolds number.

JFM classification

Waves/Free-surface Flows: Channel flow Instability: Nonlinear instability Instability: Transition to turbulence

Information

Type
Rapids
Information
Journal of Fluid Mechanics , Volume 731 , 25 September 2013 , R1
Copyright
©2013 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Aida, H., Tsukahara, T. & Kawaguchi, Y. 2011 Development of a turbulent spot into a stripe pattern in plane Poiseuille flow. In Proceedings of Seventh Symposium on Turbulence and Shear Flow Phenomena, Ottawa, Volume 3.Google Scholar
Alavyoon, F., Henningson, D. S. & Alfredsson, P. H. 1986 Turbulent spots in plane Poiseuille flow–flow visualization. Phys. Fluids 29, 1328–1331.CrossRefGoogle Scholar
Barkley, D. 2011 Simplifying the complexity of pipe flow. Phys. Rev. E 84, 016309.Google Scholar
Carlson, D. R., Widnall, S. E. & Peeters, M. F. 1982 Flow-visualization study of transition in plane Poiseuille flow. J. Fluid Mech. 121, 487–505.Google Scholar
van Doorne, C. W. H. & Westerweel, J. 2009 The flow structure of a puff. Phil. Trans. R. Soc. Lond. A 367, 489–507.Google ScholarPubMed
Duguet, Y., Le Maître, O. & Schlatter, P. 2011 Stochastic and deterministic motion of a laminar-turbulent front in a spanwisely extended Couette flow. Phys. Rev. E 84, 066315.Google Scholar
Duguet, Y. & Schlatter, P. 2013 Oblique laminar-turbulent interfaces in plane shear flows. Phys. Rev. Lett. 110, 034502.Google Scholar
Duguet, Y., Willis, A. P. & Kerswell, R. R. 2010 Slug genesis in cylindrical pipe flow. J. Fluid Mech. 663, 180–208.CrossRefGoogle Scholar
Duriez, T., Aider, J. L. & Wesfreid, J. E. 2009 Self-sustaining process through streak generation in a flat-plate boundary layer. Phys. Rev. Lett. 103, 144502.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.Google Scholar
Emmons, H. W. 1951 The laminar-turbulent transition in a boundary layer. J. Aerosp. Sci. 18, 490–498.Google Scholar
Hall, P. & Sherwin, S. 2010 Streamwise vortices in shear flows: harbingers of transition and the skeleton of coherent structures. J. Fluid Mech. 661, 178–205.CrossRefGoogle Scholar
Henningson, D. S., Johansson, A. V. & Alfredsson, P. H. 1994 Turbulent spots in channel flows. J. Engng Maths 28, 21–42.CrossRefGoogle Scholar
Henningson, D. S. & Kim, J. 1991 On turbulent spots in plane Poiseuille flow. J. Fluid Mech. 228, 183–205.Google Scholar
Henningson, D. S., Spalart, P. & Kim, J. 1987 Numerical simulations of turbulent spots in plane Poiseuille and boundary-layer flow. Phys. Fluids 30, 2914–2917.CrossRefGoogle Scholar
Hof, B., de Lozar, A., Avila, M., Tu, X. & Schneider, T. M. 2010 Eliminating turbulence in spatially intermittent flows. Science 327, 1491–1494.CrossRefGoogle ScholarPubMed
Klingmann, B. G. B. 1992 On transition due to three-dimensional disturbances in plane Poiseuille flow. J. Fluid Mech. 240, 167–195.Google Scholar
Knobloch, E. 2008 Spatially localized structures in dissipative systems: open problems. Nonlinearity 21, T45–T60.Google Scholar
Lagha, M. & Manneville, P. 2007 Modelling of plane Couette flow. I. Large scale flow around turbulent spots. Phys. Fluids 19, 094105.Google Scholar
Lemoult, G., Aider, J. L. & Wesfreid, J. E. 2012 Experimental scaling law for the subcritical transition to turbulence in plane Poiseuille flow. Phys. Rev. E 85, 025303.Google Scholar
Lundbladh, A. & Johansson, A. V. 1991 Direct simulation of turbulent spots in plane Couette flow. J. Fluid Mech. 229, 499–516.Google Scholar
Mathew, J. & Das, A. 2000 Direct numerical simulations of spots. Curr. Sci. 79, 816–820.Google Scholar
Orszag, S. A. 1971 Accurate solution of the Orr–Sommerfeld stability equation. J. Fluid Mech. 50, 689–703.CrossRefGoogle Scholar
Prigent, A., Grégoire, G., Chaté, H. & Dauchot, O. 2003 Long-wavelength modulation of turbulent shear flows. Physica D 174, 100–113.Google Scholar
Reddy, S. C. & Henningson, D. S. 1993 Energy growth in viscous channel flows. J. Fluid Mech. 252, 209–209.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 flows. J. Fluid Mech. 365, 269–303.Google Scholar
Reynolds, O. 1883 An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels. Phil. Trans. R. Soc. Lond. 174, 935–982.Google Scholar
Riley, J. J. & Gad-el Hak, M. 1985 The dynamics of turbulent spots. In Frontiers in Fluid Mechanics (ed. Davis, S. H. & Lumley, J. L.), pp. 123–155. Springer.Google Scholar
Schumacher, J. & Eckhardt, B. 2001 Evolution of turbulent spots in a parallel shear flow. Phys. Rev. E 63, 046307.Google Scholar
Seki, D. & Matsubara, M. 2012 Experimental investigation of relaminarizing and transitional channel flows. Phys. Fluids 24, 124102.Google Scholar
Shimizu, M. & Kida, S. 2009 A driving mechanism of a turbulent puff in pipe flow. Fluid Dyn. Res. 41, 045501.Google Scholar
Takeishi, K., Kawahara, G., Uhlmann, M., Pinelli, A. & Goto, S. 2012 Puff-spot transition in rectangular-duct flow. In Proceedings of JSST 2012 International Conference on Simulation Technology in Kobe, Japan, p. 197.Google Scholar
Trefethen, L. N., Trefethen, A. E., Reddy, S. C. & Driscoll, T. A. 1993 Hydrodynamic stability without eigenvalues. Science 261, 578–584.Google Scholar
Tsukahara, T., Seki, Y., Kawamura, H. & Tochio, D. 2005 DNS of turbulent channel flow with very low Reynolds numbers. In Proceedings of Fourth International Symposium on Turbulence and Shear Flow Phenomena, Williamsburg, Volume 3, pp. 935–940.Google Scholar
Tuckerman, L. S. & Barkley, D. 2011 Patterns and dynamics in transitional plane couette flow. Phys. Fluids 23, 041301.Google Scholar
Waleffe, F. 1997 On a self-sustaining process in shear flows. Phys. Fluids 9, 883–900.Google Scholar

Lemoult et al. supplementary movie

This movie presents the instantaneous small scales streamwise fluctuations $\tilde{u}$ for $Re=2000$ and $0<t^*<170$. Arrows represents the large scale flow field. Due to the finite size of the observation window, the gray area at the start and end, corresponds to boundaries of this window.

Download Lemoult et al. supplementary movie(Video)
Video 4.2 MB