“…Nevertheless, a noticeable difference can be observed in the decay process, as shown in figure 2( e ). Firstly, the streaks at the downstream end of the band appear to be tilted at much smaller angles with respect to the streamwise direction, a possible result of a reduced inflectional instability at the downstream end (Wu & Song 2022). Secondly, the streaks away from the downstream end show less wiggling and fewer smaller structures, indicating weakened turbulent activities.…”
Section: Resultsmentioning
confidence: 99%
“…Paranjape (2019) and Mukund et al (2021) reported similar phenomena for transient turbulent bands at Re 640. Wu & Song (2022) proposed that the decrease of the tilt angle of the streaks and the propagating speeds of the downstream end is a result of the weakened linear instability associated with the local mean flow, which was proposed to be responsible for the generation of wave-like velocity streaks and turbulence at the downstream end (Song & Xiao 2020;Xiao & Song 2020a). Weakened linear instability gives smaller tilt angle of the flow structure and wave speed of the most unstable eigenmode, which is qualitatively consistent with the observed phenomena for a decaying band.…”
Section: Appendix a Decay Of A Turbulent Bandmentioning
confidence: 99%
“…Kanazawa (2018) proposed that a nonlinear relative periodic orbit is embedded at the downstream end of a turbulent band, generating velocity streaks and vortices periodically; while Xiao & Song (2020 a ) and Song & Xiao (2020) reported an inflectional instability associated with the local mean flow as the mechanism for turbulence generation there. However, a turbulent band immediately starts to decay if this mechanism is interrupted when the downstream end collides either with other turbulent bands (Shimizu & Manneville 2019; Song & Xiao 2020) or with the channel sidewall (Paranjape 2019; Kohyama, Sano & Tsukahara 2022; Wu & Song 2022). Free of disruption, a turbulent band even can be maintained down to , if the mechanism at the downstream end is maintained with some external body forces (Song & Xiao 2020).…”
It has been reported that a fully localized turbulent band in channel flow becomes sustained when the Reynolds number is above a threshold. Here we show evidence that turbulent bands are of a transient nature instead. When the band length is controlled to be fixed, the lifetime of turbulent bands appears to be stochastic and exponentially distributed, a sign of a memoryless transient nature. Besides increasing with the Reynolds number, the mean lifetime also strongly increases with the band length. Given that the band length always changes over time in real channel flow, this size dependence may translate into a time dependence, which needs to be taken into account when clarifying the relationship between channel flow transition and the directed percolation universality class.
“…Nevertheless, a noticeable difference can be observed in the decay process, as shown in figure 2( e ). Firstly, the streaks at the downstream end of the band appear to be tilted at much smaller angles with respect to the streamwise direction, a possible result of a reduced inflectional instability at the downstream end (Wu & Song 2022). Secondly, the streaks away from the downstream end show less wiggling and fewer smaller structures, indicating weakened turbulent activities.…”
Section: Resultsmentioning
confidence: 99%
“…Paranjape (2019) and Mukund et al (2021) reported similar phenomena for transient turbulent bands at Re 640. Wu & Song (2022) proposed that the decrease of the tilt angle of the streaks and the propagating speeds of the downstream end is a result of the weakened linear instability associated with the local mean flow, which was proposed to be responsible for the generation of wave-like velocity streaks and turbulence at the downstream end (Song & Xiao 2020;Xiao & Song 2020a). Weakened linear instability gives smaller tilt angle of the flow structure and wave speed of the most unstable eigenmode, which is qualitatively consistent with the observed phenomena for a decaying band.…”
Section: Appendix a Decay Of A Turbulent Bandmentioning
confidence: 99%
“…Kanazawa (2018) proposed that a nonlinear relative periodic orbit is embedded at the downstream end of a turbulent band, generating velocity streaks and vortices periodically; while Xiao & Song (2020 a ) and Song & Xiao (2020) reported an inflectional instability associated with the local mean flow as the mechanism for turbulence generation there. However, a turbulent band immediately starts to decay if this mechanism is interrupted when the downstream end collides either with other turbulent bands (Shimizu & Manneville 2019; Song & Xiao 2020) or with the channel sidewall (Paranjape 2019; Kohyama, Sano & Tsukahara 2022; Wu & Song 2022). Free of disruption, a turbulent band even can be maintained down to , if the mechanism at the downstream end is maintained with some external body forces (Song & Xiao 2020).…”
It has been reported that a fully localized turbulent band in channel flow becomes sustained when the Reynolds number is above a threshold. Here we show evidence that turbulent bands are of a transient nature instead. When the band length is controlled to be fixed, the lifetime of turbulent bands appears to be stochastic and exponentially distributed, a sign of a memoryless transient nature. Besides increasing with the Reynolds number, the mean lifetime also strongly increases with the band length. Given that the band length always changes over time in real channel flow, this size dependence may translate into a time dependence, which needs to be taken into account when clarifying the relationship between channel flow transition and the directed percolation universality class.
“…In that case, the end-walls greatly perturb the laminar base state and may trigger subcritical transition [80] or even result in linear instabilities [90][91][92]. For channel flow, it has been recently shown that end-walls destabilize laminar-turbulent bands and can cause relaminarization [93,94].…”
Section: (A) Spiral Turbulence and Turbulent Spotsmentioning
confidence: 99%
“…In that case, the end-walls greatly perturb the laminar base state and may trigger subcritical transition [80] or even result in linear instabilities [90–92]. For channel flow, it has been recently shown that end-walls destabilize laminar–turbulent bands and can cause relaminarization [93,94]. Figure 6Laminarization boundary of turbulent spots in terms of the critical shear Reynolds number (ReS) as a function of the rotation number (RΩ).…”
Section: Subcritical Route To Turbulencementioning
Fluid flows between rotating concentric cylinders exhibit two distinct routes to turbulence. In flows dominated by inner-cylinder rotation, a sequence of linear instabilities leads to temporally chaotic dynamics as the rotation speed is increased. The resulting flow patterns occupy the whole system and sequentially lose spatial symmetry and coherence in the transition process. In flows dominated by outer-cylinder rotation, the transition is abrupt and leads directly to turbulent flow regions that compete with laminar ones. We here review the main features of these two routes to turbulence. Bifurcation theory rationalizes the origin of temporal chaos in both cases. However, the catastrophic transition of flows dominated by outer-cylinder rotation can only be understood by accounting for the spatial proliferation of turbulent regions with a statistical approach. We stress the role of the rotation number (the ratio of Coriolis to inertial forces) and show that it determines the lower border for the existence of intermittent laminar–turbulent patterns.
This article is part of the theme issue ‘Taylor–Couette and related flows on the centennial of Taylor’s seminal
Philosophical Transactions
paper (part 2)’.
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