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The growth mechanism of turbulent bands in channel flow at low Reynolds numbers

Published online by Cambridge University Press:  20 November 2019

Xiangkai Xiao  and
Baofang Song Open the ORCID record for Baofang Song [Opens in a new window]
Xiangkai Xiao
Affiliation:
Center for Applied Mathematics, Tianjin University, Tianjin300072, China
Baofang Song*
Affiliation:
Center for Applied Mathematics, Tianjin University, Tianjin300072, China
*
†Email address for correspondence: [email protected]
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Abstract

In this work, we carried out direct numerical simulations in large channel domains and studied the kinematics and dynamics of fully localised turbulent bands at Reynolds number $Re=750$. Our results show that the downstream end of the band features fast streak generation and travels into the adjacent laminar flow, whereas streaks at the upstream end decay continually and more slowly. This asymmetry is responsible for the transverse growth of the band. We particularly investigated the mechanism of streak generation at the downstream end, which drives the growth of the band. We identified a spanwise inflectional instability associated with the local mean flow near the downstream end, and our results strongly suggest that this instability is responsible for the streak generation and ultimately for the growth of the band. Based on our study, we propose a possible self-sustaining mechanism of fully localised turbulent bands at low Reynolds numbers in channel flow.

JFM classification

Instability: Transition to turbulence Nonlinear Dynamical Systems: Pattern formation Turbulent Flows: Turbulence simulation
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 883 , 25 January 2020 , R1
Copyright
© 2019 Cambridge University Press

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References

Alavyoon, F., Henningson, D. S. & Alfredsson, P. H. 1986 Turbulent spots in plane Poiseuille flow – flow visualization. Phys. Fluids 29, 1328.CrossRefGoogle Scholar
Barkley, D. & Tuckerman, L. S. 2005 Computational study of turbulent laminar patterns in Couette flow. Phys. Rev. Lett. 94, 014502.CrossRefGoogle ScholarPubMed
Carlson, D. R., Widnall, S. E. & Peeters, M. F. 1982 A flow-visualization study of spots in plane Poiseuille flow. J. Fluid Mech. 121, 487–505.CrossRefGoogle Scholar
Chantry, M., Tuckerman, L. S. & Barkley, D. 2017 Universal continuous transition to turbulence in a planar shear flow. J. Fluid Mech. 824, R1.CrossRefGoogle Scholar
Coles, D. 1965 Transition in circular Couette flow. J. Fluid Mech. 3, 385–425.CrossRefGoogle Scholar
Dauchaot, O. & Daviaud, F. 1995 Finite amplitude perturbation and spots growth mechanism in plane Couette flow. Phys. Fluids 7, 335.CrossRefGoogle 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
Henningson, D. S 1989 Wave growth and spreading of a turbulent spot in plane Poiseuille flow. Phys. Fluids A 1, 1876.CrossRefGoogle Scholar
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. & Kim, J. 1991 On turbulent spots in plane Poiseuille flow. J. Fluid Mech. 228, 183–205.Google 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
Hugues, S. & Randriamampianina, A. 1998 An improved projection scheme applied to pseudospectral methods for the incompressible Navier–Stokes equations. Intl J. Numer. Meth. Fluids 28, 501–521.3.0.CO;2-S>CrossRefGoogle Scholar
Kanazawa, T.2018 Lifetime and growing process of localized turbulence in plane channel flow. PhD thesis, Osaka University.Google Scholar
Lemoult, G., Shi, L., Avila, K., Jalikop, S. V., Avila, M. & Hof, B. 2016 Directed percolation phase transition to sustained turbulence in Couette flow. Nat. Phys. 12, 254–258.CrossRefGoogle Scholar
Li, F. & Widnall, S. E. 1989 Wave patterns in plane Poiseuille flow created by concentrated disturbances. J. Fluid Mech. 208, 639–656.CrossRefGoogle Scholar
Mukund, V. & Hof, B. 2018 The critical point of the transition to turbulence in pipe flow. J. Fluid Mech. 839, 76–94.CrossRefGoogle Scholar
Prigent, A., Gregoire, G., Chate, H., Dauchot, O. & van Saarloos, W. 2002 Large-scale finite-wavelength modulation within turbulent shear flows. Phys. Rev. Lett. 89, 014501.CrossRefGoogle ScholarPubMed
Rolland, J. 2015 Formation of spanwise vorticity in oblique turbulent bands of transitional plane Couette flow. Part 1. Numerical experiments. Eur. J. Mech. (B/Fluids) 50, 52–59.CrossRefGoogle Scholar
Rolland, J. 2016 Formation of spanwise vorticity in oblique turbulent bands of transitional plane Couette flow. Part 2. Modelling and stability analysis. Eur. J. Mech. (B/Fluids) 56, 13–27.CrossRefGoogle Scholar
Sano, M. & Tamai, K. 2016 A universal transition to turbulence in channel flow. Nat. Phys. 12, 249–253.CrossRefGoogle Scholar
Shimizu, M. & Kida, S. 2009 A driving mechanism of a turbulent puff in pipe flow. Fluid Dyn. Res. 41 (4), 045501.CrossRefGoogle Scholar
Shimizu, M. & Manneville, P.2018 Bifurcations to turbulence in transitional channel flow. arXiv:1808.06479v1.CrossRefGoogle Scholar
Tao, J. J., Eckhardt, B. & Xiong, X. M. 2018 Extended localized structures and the onset of turbulence in channel flow. Phys. Rev. Fluids 3, 011902.CrossRefGoogle Scholar
Trefethen, L. N. 2000 Spectral Methods in Matlab. SIAM.CrossRefGoogle Scholar
Tsukahara, T., Kawaguchi, Y. & Kawamura, H.2014 An experimental study on turbulent-stripe structure in transitional channel flow. arXiv:1406.1378.Google Scholar
Tsukahara, T. & Kawamura, H.2014 Turbulent heat transfer in a channel flow at transitional Reynolds numbers. arXiv:1406.0959v1.Google Scholar
Tsukahara, T., Seki, Y., Kawamura, H. & Tochio, D. 2005 DNS of turbulent channel flow at very low Reynolds numbers. In Proceedings of Fourth International Symposium on Turbulence and Shear Flow Phenomena, pp. 935–940. Williamsburg.Google Scholar
Tuckerman, L. S., Kreilos, T., Shrobsdorff, H., Schneider, T. M. & Gibson, J. F. 2014 Turbulent–laminar patterns in plane Poiseuille flow. Phys. Fluids 26, 114103.CrossRefGoogle Scholar
Willis, A. P. 2017 The Openpipeflow Navier–Stokes solver. SoftwareX 6, 124–127.CrossRefGoogle Scholar
Xiong, X. M., Tao, J., Chen, S. & Brandt, L. 2015 Turbulent bands in plane-Poiseuille flow at moderate Reynolds numbers. Phys. Fluids 27, 041702.CrossRefGoogle Scholar

Xiao et al. supplementary movie 1

The visualisation of streak generation at the stripe head. The contours of streamwise velocity fluctuations are plotted in the x-z cut-plane at y=-0.5. Yellow represents higher velocity and blue represents lower velocity compared to the base flow at the same y position. The frame of reference is co-moving with the stripe head.

Download Xiao et al. supplementary movie 1(Video)
Video 2.9 MB

Xiao et al. supplementary movie 2

The temporal change of the profile of the spanwise velocity spatially averaged in region I (see Fig. 4(a) in the manuscript) at the stripe head.

Download Xiao et al. supplementary movie 2(Video)
Video 1.2 MB