Hostname: page-component-8448b6f56d-t5pn6 Total loading time: 0 Render date: 2024-04-18T19:21:31.663Z Has data issue: false hasContentIssue false
  • English
  • Français

Lagrangian approach to laminar–turbulent interfaces in transitional pipe flow

Published online by Cambridge University Press:  16 April 2013

Markus Holzner ,
Baofang Song ,
Marc Avila  and
Björn Hof
Markus Holzner*
Affiliation:
Max Planck Institute for Dynamics and Self-Organisation, Bunsenstraße 10, 37073 Göttingen, Germany
Baofang Song
Affiliation:
Max Planck Institute for Dynamics and Self-Organisation, Bunsenstraße 10, 37073 Göttingen, Germany
Marc Avila
Affiliation:
Max Planck Institute for Dynamics and Self-Organisation, Bunsenstraße 10, 37073 Göttingen, Germany Institute of Fluid Mechanics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstraße 4, 91058 Erlangen, Germany
Björn Hof
Affiliation:
Max Planck Institute for Dynamics and Self-Organisation, Bunsenstraße 10, 37073 Göttingen, Germany
*
†Email address for correspondence: holzner@ifu.baug.ethz.ch
Get access Rights & Permissions [Opens in a new window]

Abstract

Transition in shear flows is characterized by localized turbulent regions embedded in the surrounding laminar flow. These so-called turbulent spots or puffs are observed in a variety of shear flows and in certain Reynolds-number regimes, and they are advected by the flow while keeping their characteristic length. We show here for the case of pipe flow that this seemingly passive advection of turbulent puffs involves continuous entrainment and relaminarization of laminar and turbulent fluid across strongly convoluted interfaces. Surprisingly, interface areas are almost two orders of magnitude larger than the pipe cross-section, while local entrainment velocities are much smaller than the mean speed. Even though these velocities were shown to be small and proportional to the Kolmogorov velocity scale (in agreement with a prediction by Corrsin) in a flow without mean shear before, we find that, in pipe flow, local entrainment velocities are about an order of magnitude smaller than this scale. The Lagrangian method used to study the dynamics of the laminar–turbulent interfaces allows accurate determination of the leading and trailing edge speeds. However, to resolve the highly complex interface dynamics requires much higher numerical resolutions than for ordinary turbulent flows. This method also reveals that the volume flux across the leading edge has the same radial dependence but the opposite sign as that across the trailing edge, and it is this symmetry that is responsible for the puff shape remaining constant.

JFM classification

Instability: Instability Nonlinear Dynamical Systems: Pattern formation Instability: Transition to turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 723 , 25 May 2013 , pp. 140 - 162
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.)

References

Avila, K., Moxey, D., De Lozar, A., Avila, M., Barkley, D. & Hof, B. 2011 The onset of turbulence in pipe flow. Science 333 (6039), 192–196.Google Scholar
Avila, M., Willis, A. P. & Hof, B. 2010 On the transient nature of localized pipe flow turbulence. J. Fluid Mech. 646, 127–136.Google Scholar
Bandyopadhyay, P. R. 1986 Aspects of the equilibrium puff in transitional pipe flow. J. Fluid Mech. 163, 439–458.Google Scholar
Bisset, D. K., Hunt, J. C. R. & Rogers, M. M. 2002 The turbulent/non-turbulent interface bounding a far wake. J. Fluid Mech. 451, 382–410.Google Scholar
Catrakis, H. J. & Dimotakis, P. E. 1996 Mixing in turbulent jets: scalar measures and isosurface geometry. J. Fluid Mech. 317, 369–406.Google Scholar
Corrsin, S. & Kistler, A. L. 1955 The free stream boundaries of turbulent flows. NACA Tech. Rep. TN-3133, TR-1244.Google Scholar
Darbyshire, A. G. & Mullin, T. 1995 Transition to turbulence in constant-mass-flux pipe flow. J. Fluid Mech. 289, 83–114.Google Scholar
van Doorne, C. W. H. & Westerweel, J. 2009 The flow structure of a puff. Phil. Trans. R. Soc. A 367, 489.CrossRefGoogle ScholarPubMed
Dopazo, C. 1977 On conditioned averages for intermittent turbulent flows. J. Fluid Mech. 81, 433–438.CrossRefGoogle Scholar
Duguet, Y., Willis, A. P. & Kerswell, R. R. 2010 Slug genesis in cylindrical pipe flow. J. Fluid Mech. 663, 180–208.Google Scholar
Hof, B., de Lozar, A., Avila, M., Tu, X. & Schneider, T. 2010 Eliminating turbulence in spatially intermittent flows. Science 327, 1491–1494.CrossRefGoogle ScholarPubMed
Hof, B., de Lozar, A., Kuik, D. J. & Westerweel, J. 2008 Repeller or attractor? Selecting the dynamical model for the onset of turbulence in pipe flow. Phys. Rev. Lett. 101 (21), 214501.Google Scholar
Hof, B., Westerweel, J., Schneider, T. M. & Eckhardt, B. 2006 Finite lifetime of turbulence in shear flows. Nature 443 (7107), 59–62.Google Scholar
Holzner, M., Avila, A., de Lozar, A. & Hof, B. 2011 Lagrangian approach to turbulent puffs in pipe flow. J. Phys. Conf. Ser. 318, 052031 (European Turbulence Conference, ETC 13).Google Scholar
Holzner, M., Liberzon, A., Nikitin, N., Lüthi, B., Kinzelbach, W. & Tsinober, A. 2008 A Lagrangian investigation of the small scale features of turbulent entrainment through particle tracking and direct numerical simulation. J. Fluid Mech. 598, 465–475.Google Scholar
Holzner, M. & Lüthi, B. 2011 Laminar superlayer at the turbulence boundary. Phys. Rev. Lett. 106, 134503.Google Scholar
Lindgren, E. R. 1969 Propagation velocity of turbulent slugs and streaks in transition pipe flow. Phys. Fluids 12 (2), 418–425.Google Scholar
Moxey, D. & Barkley, D. 2010 Distinct large-scale turbulent–laminar states in transitional pipe flow. Proc. Natl Acad. Sci. USA 107 (18), 8091–8096.Google Scholar
Rotta, J. 1956 Experimenteller Beitrag zur Entstehung turbulenter Strömung im Rohr. Ing.-Arch. 24, 258–281.CrossRefGoogle Scholar
Shan, H., Ma, B., Zhang, Z. & Niewstadt, F. T. M. 1999 Direct numerical simulation of a puff and a slug in transitional cylindrical pipe flow. J. Fluid Mech. 387, 39–60.Google Scholar
Shimizu, M. & Kida, S. 2009 A driving mechanism of a turbulent puff in pipe flow. Fluid Dyn. Res. 41, 045501.CrossRefGoogle Scholar
Sreenivasan, K. R. 1991 Fractals and multifractals in fluid turbulence. Annu. Rev. Fluid Mech. 23, 539–604.Google Scholar
Townsend, A. A. 1966 The mechanism of entrainment in free turbulent flows. J. Fluid Mech. 26, 689–715.Google Scholar
Willis, A. P. & Kerswell, R. R. 2007 Critical behavior in the relaminarization of localized turbulence in pipe flow. Phys. Rev. Lett. 98 (1), 014501.Google Scholar
Willis, A. P. & Kerswell, R. R. 2009 Turbulent dynamics of pipe flow captured in a reduced model: puff relaminarization and localized edge states. J. Fluid Mech. 619, 213–233.Google Scholar
Wolf, M., Lüthi, B., Holzner, M., Krug, D., Kinzelbach, W. & Tsinober, A. 2012 Investigations on the local entrainment velocity in a turbulent jet. Phys. Fluids 24, 105110.Google Scholar
Wygnanski, I. J. & Champagne, F. H. 1973 On transition in a pipe. Part 1. The origin of puffs and slugs and the flow in a turbulent slug. J. Fluid Mech. 59, 281–335.Google Scholar
Wygnanski, I. J., Sokolov, M. & Friedman, D. 1975 On transition in a pipe. Part 2. The equilibrium puff. J. Fluid Mech. 69, 283–304.Google Scholar