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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: baofang_song@tju.edu.cn
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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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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