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Transient characteristics of fully localised turbulence in transitional channel flow
Published online by Cambridge University Press: 14 April 2025
Abstract
The temporal characteristics of fully localised turbulent bands in transitional channel flow remains unclear due to the difficulty in resolving the large length and time scales involved. Here, we tackle this problem by performing statistical lifetime studies in sufficiently large computational domains. The results show signs of stochastic memoryless decay of a fully localised band, suggesting a chaotic-saddle behaviour of the entire band as a coherent entity. Although the mean lifetime of a turbulent band was reported to increase with the band length, our data suggest that it saturates at a certain length. This saturation results in a characteristic lifetime for a fully developed band with a changing length due to the intermittent chipping and decay of turbulence at the upstream end. This memoryless behaviour is observed down to Reynolds number 
$Re=630$ in our study and we propose that the onset of the memoryless behaviour is in the range of 
$Re\simeq 620{-}630$. Our data also show that the time it takes for a perturbed flow to enter the saddle, i.e. to start behaving memorylessly, can be thousands of convective time units, which is comparable to the maximum achievable observation time in existing channel set-ups and may pose difficulties for experiments.
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Wu and Song supplementary material movie 1
The decay of a turbulent band at Re=640 in a large computation domain without an artificial damping, i.e. the band can develop freely without any artificial constraints. The size and aspect ratio of the domain were selected to avoid the tail-head interaction while keeping the domain size minimum. Note that this domain size is much larger than the one with a damping region as shown in the main text. The flow is from left to right and the simulation was carried out in a moving frame of reference with a streamwise speed of 0.85 and a spanwise speed of 0.1 (in the negative direction of the z axis). The length of the band underwent large variations due to the band chipping at the upstream end. The band started decaying at t ≈ 5900, since when the head of the band significantly slowed down.
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3 MB
Wu and Song supplementary material movie 2
The decay of a turbulent band at Re=640 in the moving frame reference with damping. The damping region is between z=130 and 140 as explained in the main text. Streamwise velocity fluctuations are visualized as the colors, where red color represents high speed region and blue color represents low speed region. The band starts to decay at approximately t=1800.
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5.1 MB
Wu and Song supplementary material movie 3
The decay of a turbulent band at Re=640 in the moving frame reference with damping. The damping region is between z=130 and 140 as explained in the main text. Streamwise velocity fluctuations are visualized as the colors, where red color represents high speed region and blue color represents low speed region. The band starts to decay at approximately t=4600.
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5.9 MB