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Growth dynamics of turbulent spots in plane Couette flow

Published online by Cambridge University Press:  18 April 2017

Marie Couliou Open the ORCID record for Marie Couliou [Opens in a new window]  and
Romain Monchaux
Marie Couliou
Affiliation:
IMSIA, ENSTA ParisTech, CNRS, CEA, EDF, Université Paris-Saclay, 828 Boulevard des Maréchaux, 91762 Palaiseau CEDEX, France
Romain Monchaux*
Affiliation:
IMSIA, ENSTA ParisTech, CNRS, CEA, EDF, Université Paris-Saclay, 828 Boulevard des Maréchaux, 91762 Palaiseau CEDEX, France
*
†Email address for correspondence: [email protected]
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Abstract

We experimentally and numerically investigate the temporal aspects of turbulent spots spreading in a plane Couette flow for transitional Reynolds numbers between 300 and 450. Spot growth rate, spot advection rate and large-scale flow intensity are measured as a function of time and Reynolds number. All these quantities show similar dynamics clarifying the role played by large-scale flows in the advection of the turbulent spot. The contributions of each possible growth mechanism, that is, growth induced by large-scale advection or growth by destabilization, are discussed for the different stages of the spot growth. A scenario that gathers all these elements is providing a better understanding of the growth dynamics of turbulent spots in plane Couette flow that should possibly apply to other extended shear flows.

JFM classification

Instability: Instability Instability: Transition to turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 819 , 25 May 2017 , pp. 1 - 20
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Copyright
© 2017 Cambridge University Press 

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References

Barkley, D., Song, B., Mukund, V., Lemoult, G., Avila, M. & Hof, B. 2015 The rise of fully turbulent flow. Nature 526, 550–553.CrossRefGoogle ScholarPubMed
Barkley, D. & Tuckerman, L. S. 2005 Computational study of turbulent–laminar patterns in Couette flow. Phys. Rev. Lett. 94, 014502.CrossRefGoogle ScholarPubMed
Barkley, D. & Tuckerman, L. S. 2007 Mean flow of turbulent–laminar patterns in plane Couette flow. J. Fluid Mech. 576, 109–137.CrossRefGoogle Scholar
Bottin, S., Dauchot, O. & Daviaud, F. 1997 Intermittency in a locally forced plane Couette flow. Phys. Rev. Lett. 79, 4377.CrossRefGoogle Scholar
Bottin, S., Dauchot, O., Daviaud, F. & Manneville, P. 1998 Experimental evidence of streamwise vortices as finite amplitude solutions in transitional plane Couette flow. Phys. Fluids 10, 2597–2607.CrossRefGoogle Scholar
Chantry, M., Tuckerman, L. S. & Barkley, D. 2016 Turbulent–laminar patterns in shear flows without walls. J. Fluid Mech. 791, R8.CrossRefGoogle Scholar
Coles, D. 1965 Transition in circular Couette flow. J. Fluid Mech. 21, 385–425.CrossRefGoogle Scholar
Couliou, M. & Monchaux, R. 2015 Large scale flows in transitional plane Couette flow: a key ingredient of the spot growth mechanism. Phys. Fluids 27, 034101.CrossRefGoogle Scholar
Couliou, M. & Monchaux, R. 2016 Spreading of turbulence in plane Couette flow. Phys. Rev. E 93, 013108.Google ScholarPubMed
Dauchot, O. & Daviaud, F. 1995 Finite amplitude perturbation and spots growth mechanism in plane Couette flow. Phys. Fluids 7, 335–343.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
Duguet, Y., Schlatter, P. & Henningson, D. S. 2010 Formation of turbulent patterns near the onset of transition in plane Couette flow. J. Fluid Mech. 650, 119–129.CrossRefGoogle Scholar
Emmons, H. W. 1951 The laminar–turbulent transition in a boundary layer. Part 1. J. Aerosp. Sci. 18, 490–498.Google Scholar
Gad-El-Hak, M., Blackwelderf, R. F. & Riley, J. 1981 On the growth of turbulent regions in laminar boundary layers. J. Fluid Mech. 110, 73–95.CrossRefGoogle Scholar
Gibson, J. F.2014 Channelflow: a spectral Navier–Stokes simulator in $\text{C}^{++}$ . Tech. Rep. University of New Hampshire; Channelflow.org.Google Scholar
Gibson, J. F., Halcrow, J. & Cvitanović, P. 2008 Visualizing the geometry of state space in plane Couette flow. J. Fluid Mech. 611, 107–130.CrossRefGoogle Scholar
Hashimoto, S., Hasobe, A., Tsukahara, T., Kawaguchi, Y. & Kawamura, H. 2009 An experimental study on turbulent-stripe structure in transitional channel flow. In Proceedings of the Sixth International Symposium on Turbulence, Heat and Mass Transfer (ed. Hanjalić, K., Nagano, Y. & Jakirlić, S.), pp. 193–196. Begell House.Google Scholar
Hegseth, J. J. 1996 Turbulent spots in plane Couette flow. Phys. Rev. E 54, 4915–4923.Google ScholarPubMed
Henningson, D. S. & Alfredsson, P. H. 1987 The wave structure of turbulent spots in plane Poiseuille flow. J. Fluid Mech. 178, 405–421.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
Lagha, M. & Manneville, P. 2007 Modeling 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. 2013 Turbulent spots in a channel: large-scale flow and self-sustainability. J. Fluid Mech. 731, R1.CrossRefGoogle Scholar
Lundbladh, A. & Johansson, A. V. 1991 Direct simulation of turbulent spots in plane Couette flow. J. Fluid Mech. 229, 499–516.CrossRefGoogle Scholar
Manneville, P.2015 Towards a model of large scale dynamics in transitional wall-bounded flows, arXiv:1504.00664.Google Scholar
Philip, J. & Manneville, P. 2011 From temporal to spatiotemporal dynamics in transitional plane Couette flow. Phys. Rev. E 83, 036308.CrossRefGoogle ScholarPubMed
Prigent, A. & Dauchot, O. 2005 Transition to versus from turbulence in subcritical Couette flows. In IUATM Symposium on Laminar–Turbulent Transition and Finite Amplitude Solutions, pp. 195–219. Springer.CrossRefGoogle Scholar
Prigent, A., Grégoire, G., Chaté, H., Dauchot, O. & van Saarloos, W. 2002 Large-scale finite-wavelength modulation within turbulent shear flows. Phys. Rev. Lett. 89, 014501.CrossRefGoogle ScholarPubMed
Schumacher, J. & Eckhardt, B. 2001 Evolution of turbulent spots in a parallel shear flow. Phys. Rev. E 63, 046307.Google Scholar
Tillmark, N. 1995 On the spreading mechanisms of a turbulent spot in plane Couette flow. Eur. Phys. Lett. 32, 481–485.CrossRefGoogle Scholar
Tillmark, N. & Alfredsson, P. H. 1992 Experiments on transition in plane Couette flow. J. Fluid Mech. 235, 89–102.CrossRefGoogle Scholar
Tuckerman, L. S., Barkley, D. & Dauchot, O. 2008 Statistical analysis of the transition to turbulent–laminar banded patterns in plane Couette flow. J. Phys.: Conf. Ser. 137, 012029.Google Scholar
Tuckerman, L. S., Kreilos, T., Schrobsdorff, H., Schneider, T. M. & Gibson, J. F. 2014 Turbulent–laminar patterns in plane Poiseuille flow. Phys. Fluids 26, 114103.CrossRefGoogle Scholar
Van Atta, C. 1966 Exploratory measurements in spiral turbulence. J. Fluid Mech. 25, 495–512.CrossRefGoogle Scholar