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

*(English)*Zbl 1430.76322Summary: 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.

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\textit{X. Xiao} and \textit{B. Song}, J. Fluid Mech. 883, Paper No. R1, 14 p. (2020; Zbl 1430.76322)

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[1] | Alavyoon, F., Henningson, D. S. & Alfredsson, P. H.1986Turbulent spots in plane Poiseuille flow – flow visualization. Phys. Fluids29, 1328. |

[2] | Barkley, D. & Tuckerman, L. S.2005Computational study of turbulent laminar patterns in Couette flow. Phys. Rev. Lett.94, 014502. · Zbl 1124.76018 |

[3] | Carlson, D. R., Widnall, S. E. & Peeters, M. F.1982A flow-visualization study of spots in plane Poiseuille flow. J. Fluid Mech.121, 487-505. |

[4] | Chantry, M., Tuckerman, L. S. & Barkley, D.2017Universal continuous transition to turbulence in a planar shear flow. J. Fluid Mech.824, R1. · Zbl 1374.76085 |

[5] | Coles, D.1965Transition in circular Couette flow. J. Fluid Mech.3, 385-425. · Zbl 0134.21705 |

[6] | Dauchaot, O. & Daviaud, F.1995Finite amplitude perturbation and spots growth mechanism in plane Couette flow. Phys. Fluids7, 335. |

[7] | Duguet, Y. & Schlatter, P.2013Oblique laminar–turbulent interfaces in plane shear flows. Phys. Rev. Lett.110, 034502. |

[8] | Duguet, Y., Schlatter, P. & Henningson, D. S.2010Formation of turbulent patterns near the onset of transition in plane Couette flow. J. Fluid Mech.650, 119-129. · Zbl 1189.76254 |

[9] | Henningson, D. S1989Wave growth and spreading of a turbulent spot in plane Poiseuille flow. Phys. Fluids A1, 1876. |

[10] | Henningson, D. S. & Alfredsson, P. H.1987The wave structure of turbulent spots in plane Poiseuille flow. J. Fluid Mech.178, 405-421. |

[11] | Henningson, D. S. & Kim, J.1991On turbulent spots in plane Poiseuille flow. J. Fluid Mech.228, 183-205. · Zbl 0723.76048 |

[12] | Hof, B., De Lozar, A., Avila, M., Tu, X. & Schneider, T. M.2010Eliminating turbulence in spatially intermittent flows. Science327, 1491-1494. |

[13] | Hugues, S. & Randriamampianina, A.1998An improved projection scheme applied to pseudospectral methods for the incompressible Navier-Stokes equations. Intl J. Numer. Meth. Fluids28, 501-521. · Zbl 0932.76065 |

[14] | Kanazawa, T.2018 Lifetime and growing process of localized turbulence in plane channel flow. PhD thesis, Osaka University. |

[15] | Lemoult, G., Shi, L., Avila, K., Jalikop, S. V., Avila, M. & Hof, B.2016Directed percolation phase transition to sustained turbulence in Couette flow. Nat. Phys.12, 254-258. |

[16] | Li, F. & Widnall, S. E.1989Wave patterns in plane Poiseuille flow created by concentrated disturbances. J. Fluid Mech.208, 639-656. · Zbl 0681.76055 |

[17] | Mukund, V. & Hof, B.2018The critical point of the transition to turbulence in pipe flow. J. Fluid Mech.839, 76-94. · Zbl 1419.76270 |

[18] | Prigent, A., Gregoire, G., Chate, H., Dauchot, O. & Van Saarloos, W.2002Large-scale finite-wavelength modulation within turbulent shear flows. Phys. Rev. Lett.89, 014501. · Zbl 1036.76023 |

[19] | Rolland, J.2015Formation of spanwise vorticity in oblique turbulent bands of transitional plane Couette flow. Part 1. Numerical experiments. Eur. J. Mech. (B/Fluids)50, 52-59. |

[20] | Rolland, J.2016Formation 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. |

[21] | Sano, M. & Tamai, K.2016A universal transition to turbulence in channel flow. Nat. Phys.12, 249-253. |

[22] | Shimizu, M. & Kida, S.2009A driving mechanism of a turbulent puff in pipe flow. Fluid Dyn. Res.41 (4), 045501. · Zbl 1422.76107 |

[23] | Shimizu, M. & Manneville, P.2018 Bifurcations to turbulence in transitional channel flow. . |

[24] | Tao, J. J., Eckhardt, B. & Xiong, X. M.2018Extended localized structures and the onset of turbulence in channel flow. Phys. Rev. Fluids3, 011902. |

[25] | Trefethen, L. N.2000Spectral Methods in Matlab. SIAM. · Zbl 0953.68643 |

[26] | Tsukahara, T., Kawaguchi, Y. & Kawamura, H.2014 An experimental study on turbulent-stripe structure in transitional channel flow. . |

[27] | Tsukahara, T. & Kawamura, H.2014 Turbulent heat transfer in a channel flow at transitional Reynolds numbers. . |

[28] | Tsukahara, T., Seki, Y., Kawamura, H. & Tochio, D.2005DNS 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. |

[29] | Tuckerman, L. S., Kreilos, T., Shrobsdorff, H., Schneider, T. M. & Gibson, J. F.2014Turbulent–laminar patterns in plane Poiseuille flow. Phys. Fluids26, 114103. |

[30] | Willis, A. P.2017The Openpipeflow Navier-Stokes solver. SoftwareX6, 124-127. |

[31] | Xiong, X. M., Tao, J., Chen, S. & Brandt, L.2015Turbulent bands in plane-Poiseuille flow at moderate Reynolds numbers. Phys. Fluids27, 041702. |

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