Special Issue "Intermittency in Transitional Shear Flows"

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Complexity".

Deadline for manuscript submissions: closed (31 October 2020).

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Special Issue Editor

Dr. Yohann Duguet
E-Mail Website
Guest Editor
LIMSI-CNRS, Université Paris Sud, University Paris-Saclay, F-91405 Orsay, France
Interests: instability theory; fluid dynamics; turbulence; dynamical systems

Special Issue Information

Dear Colleagues,

The transition to turbulence in fluid flows remains one of the unsolved problems of classical physics. An especially challenging configuration occurs when laminar and turbulent flows coexist in both space and time, as revealed by an ever-increasing number of experimental and computational investigations. This concerns most flows in simple geometries such as pipes, ducts, channels, and also boundary layer flows. Many issues, such as the analogy with phase coexistence in thermodynamics, the low-dimensional modeling of the spatial self-organization of the flow or its relevance in various fields of application, remain open today. This Special Issue will be an ideal opportunity to review and gather the latest progress on this fascinating interdisciplinary topic at the crossroad among hydrodynamics, complexity theory, and statistical physics.

Dr. Yohann Duguet
Guest Editor

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Keywords

  • laminar–turbulent coexistence
  • intermittency
  • shear flows
  • turbulent flow
  • transition to turbulence

Published Papers (10 papers)

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Editorial

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Editorial
Intermittency in Transitional Shear Flows
Entropy 2021, 23(3), 280; https://doi.org/10.3390/e23030280 - 26 Feb 2021
Cited by 1 | Viewed by 443
Abstract
The study of the transition from a laminar to a turbulent flow is as old as the study of turbulence itself [...] Full article
(This article belongs to the Special Issue Intermittency in Transitional Shear Flows)

Research

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Article
Second-Order Phase Transition in Counter-Rotating Taylor–Couette Flow Experiment
Entropy 2021, 23(1), 58; https://doi.org/10.3390/e23010058 - 31 Dec 2020
Cited by 3 | Viewed by 810
Abstract
In many basic shear flows, such as pipe, Couette, and channel flow, turbulence does not arise from an instability of the laminar state, and both dynamical states co-exist. With decreasing flow speed (i.e., decreasing Reynolds number) the fraction of fluid in laminar motion [...] Read more.
In many basic shear flows, such as pipe, Couette, and channel flow, turbulence does not arise from an instability of the laminar state, and both dynamical states co-exist. With decreasing flow speed (i.e., decreasing Reynolds number) the fraction of fluid in laminar motion increases while turbulence recedes and eventually the entire flow relaminarizes. The first step towards understanding the nature of this transition is to determine if the phase change is of either first or second order. In the former case, the turbulent fraction would drop discontinuously to zero as the Reynolds number decreases while in the latter the process would be continuous. For Couette flow, the flow between two parallel plates, earlier studies suggest a discontinuous scenario. In the present study we realize a Couette flow between two concentric cylinders which allows studies to be carried out in large aspect ratios and for extensive observation times. The presented measurements show that the transition in this circular Couette geometry is continuous suggesting that former studies were limited by finite size effects. A further characterization of this transition, in particular its relation to the directed percolation universality class, requires even larger system sizes than presently available. Full article
(This article belongs to the Special Issue Intermittency in Transitional Shear Flows)
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Article
Spatiotemporal Intermittency in Pulsatile Pipe Flow
Entropy 2021, 23(1), 46; https://doi.org/10.3390/e23010046 - 30 Dec 2020
Cited by 2 | Viewed by 765
Abstract
Despite its importance in cardiovascular diseases and engineering applications, turbulence in pulsatile pipe flow remains little comprehended. Important advances have been made in the recent years in understanding the transition to turbulence in such flows, but the question remains of how turbulence behaves [...] Read more.
Despite its importance in cardiovascular diseases and engineering applications, turbulence in pulsatile pipe flow remains little comprehended. Important advances have been made in the recent years in understanding the transition to turbulence in such flows, but the question remains of how turbulence behaves once triggered. In this paper, we explore the spatiotemporal intermittency of turbulence in pulsatile pipe flows at fixed Reynolds and Womersley numbers (Re=2400, Wo=8) and different pulsation amplitudes. Direct numerical simulations (DNS) were performed according to two strategies. First, we performed DNS starting from a statistically steady pipe flow. Second, we performed DNS starting from the laminar Sexl–Womersley flow and disturbed with the optimal helical perturbation according to a non-modal stability analysis. Our results show that the optimal perturbation is unable to sustain turbulence after the first pulsation period. Spatiotemporally intermittent turbulence only survives for multiple periods if puffs are triggered. We find that puffs in pulsatile pipe flow do not only take advantage of the self-sustaining lift-up mechanism, but also of the intermittent stability of the mean velocity profile. Full article
(This article belongs to the Special Issue Intermittency in Transitional Shear Flows)
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Article
Intermittency, Moments, and Friction Coefficient during the Subcritical Transition of Channel Flow
Entropy 2020, 22(12), 1399; https://doi.org/10.3390/e22121399 - 11 Dec 2020
Cited by 1 | Viewed by 642
Abstract
The intermittent distribution of localized turbulent structures is a key feature of the subcritical transitions in channel flows, which are studied in this paper with a wind channel and theoretical modeling. Entrance disturbances are introduced by small beads, and localized turbulent patches can [...] Read more.
The intermittent distribution of localized turbulent structures is a key feature of the subcritical transitions in channel flows, which are studied in this paper with a wind channel and theoretical modeling. Entrance disturbances are introduced by small beads, and localized turbulent patches can be triggered at low Reynolds numbers (Re). High turbulence intensity represents strong ability of perturbation spread, and a maximum turbulence intensity is found for every test case as Re ≥ 950, where the turbulence fraction increases abruptly with Re. Skewness can reflect the velocity defects of localized turbulent patches and is revealed to become negative when Re is as low as about 660. It is shown that the third-order moments of the midplane streamwise velocities have minima, while the corresponding forth-order moments have maxima during the transition. These kinematic extremes and different variation scenarios of the friction coefficient during the transition are explained with an intermittent structure model, where the robust localized turbulent structure is simplified as a turbulence unit, a structure whose statistical properties are only weak functions of the Reynolds number. Full article
(This article belongs to the Special Issue Intermittency in Transitional Shear Flows)
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Article
Laminar–Turbulent Intermittency in Annular Couette–Poiseuille Flow: Whether a Puff Splits or Not
Entropy 2020, 22(12), 1353; https://doi.org/10.3390/e22121353 - 30 Nov 2020
Cited by 1 | Viewed by 802
Abstract
Direct numerical simulations were carried out with an emphasis on the intermittency and localized turbulence structure occurring within the subcritical transitional regime of a concentric annular Couette–Poiseuille flow. In the annular system, the ratio of the inner to outer cylinder radius is an [...] Read more.
Direct numerical simulations were carried out with an emphasis on the intermittency and localized turbulence structure occurring within the subcritical transitional regime of a concentric annular Couette–Poiseuille flow. In the annular system, the ratio of the inner to outer cylinder radius is an important geometrical parameter affecting the large-scale nature of the intermittency. We chose a low radius ratio of 0.1 and imposed a constant pressure gradient providing practically zero shear on the inner cylinder such that the base flow was approximated to that of a circular pipe flow. Localized turbulent puffs, that is, axial uni-directional intermittencies similar to those observed in the transitional circular pipe flow, were observed in the annular Couette–Poiseuille flow. Puff splitting events were clearly observed rather far from the global critical Reynolds number, near which given puffs survived without a splitting event throughout the observation period, which was as long as 104 outer time units. The characterization as a directed-percolation universal class was also discussed. Full article
(This article belongs to the Special Issue Intermittency in Transitional Shear Flows)
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Article
Transitional Channel Flow: A Minimal Stochastic Model
Entropy 2020, 22(12), 1348; https://doi.org/10.3390/e22121348 - 29 Nov 2020
Cited by 3 | Viewed by 746
Abstract
In line with Pomeau’s conjecture about the relevance of directed percolation (DP) to turbulence onset/decay in wall-bounded flows, we propose a minimal stochastic model dedicated to the interpretation of the spatially intermittent regimes observed in channel flow before its return to laminar flow. [...] Read more.
In line with Pomeau’s conjecture about the relevance of directed percolation (DP) to turbulence onset/decay in wall-bounded flows, we propose a minimal stochastic model dedicated to the interpretation of the spatially intermittent regimes observed in channel flow before its return to laminar flow. Numerical simulations show that a regime with bands obliquely drifting in two stream-wise symmetrical directions bifurcates into an asymmetrical regime, before ultimately decaying to laminar flow. The model is expressed in terms of a probabilistic cellular automaton of evolving von Neumann neighborhoods with probabilities educed from a close examination of simulation results. It implements band propagation and the two main local processes: longitudinal splitting involving bands with the same orientation, and transversal splitting giving birth to a daughter band with an orientation opposite to that of its mother. The ultimate decay stage observed to display one-dimensional DP properties in a two-dimensional geometry is interpreted as resulting from the irrelevance of lateral spreading in the single-orientation regime. The model also reproduces the bifurcation restoring the symmetry upon variation of the probability attached to transversal splitting, which opens the way to a study of the critical properties of that bifurcation, in analogy with thermodynamic phase transitions. Full article
(This article belongs to the Special Issue Intermittency in Transitional Shear Flows)
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Article
Kinematics and Dynamics of Turbulent Bands at Low Reynolds Numbers in Channel Flow
Entropy 2020, 22(10), 1167; https://doi.org/10.3390/e22101167 - 16 Oct 2020
Cited by 2 | Viewed by 959
Abstract
Channel flow turbulence exhibits interesting spatiotemporal complexities at transitional Reynolds numbers. In this paper, we investigated some aspects of the kinematics and dynamics of fully localized turbulent bands in large flow domains. We discussed the recent advancement in the understanding of the wave-generation [...] Read more.
Channel flow turbulence exhibits interesting spatiotemporal complexities at transitional Reynolds numbers. In this paper, we investigated some aspects of the kinematics and dynamics of fully localized turbulent bands in large flow domains. We discussed the recent advancement in the understanding of the wave-generation at the downstream end of fully localized bands. Based on the discussion, we proposed a possible mechanism for the tilt direction selection. We measured the propagation speed of the downstream end and the advection speed of the low-speed streaks in the bulk of turbulent bands at various Reynolds numbers. Instead of measuring the tilt angle by treating an entire band as a tilted object as in prior studies, we proposed that, from the point of view of the formation and growth of turbulent bands, the tilt angle should be determined by the relative speed between the downstream end and the streaks in the bulk. We obtained a good agreement between our calculation of the tilt angle and the reported results in the literature at relatively low Reynolds numbers. Full article
(This article belongs to the Special Issue Intermittency in Transitional Shear Flows)
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Article
Low- and High-Drag Intermittencies in Turbulent Channel Flows
Entropy 2020, 22(10), 1126; https://doi.org/10.3390/e22101126 - 04 Oct 2020
Cited by 5 | Viewed by 938
Abstract
Recent direct numerical simulations (DNS) and experiments in turbulent channel flow have found intermittent low- and high-drag events in Newtonian fluid flows, at Reτ=uτh/ν between 70 and 100, where uτ, h and ν [...] Read more.
Recent direct numerical simulations (DNS) and experiments in turbulent channel flow have found intermittent low- and high-drag events in Newtonian fluid flows, at Reτ=uτh/ν between 70 and 100, where uτ, h and ν are the friction velocity, channel half-height and kinematic viscosity, respectively. These intervals of low-drag and high-drag have been termed “hibernating” and “hyperactive”, respectively, and in this paper, a further investigation of these intermittent events is conducted using experimental and numerical techniques. For experiments, simultaneous measurements of wall shear stress and velocity are carried out in a channel flow facility using hot-film anemometry (HFA) and laser Doppler velocimetry (LDV), respectively, for Reτ between 70 and 250. For numerical simulations, DNS of a channel flow is performed in an extended domain at Reτ = 70 and 85. These intermittent events are selected by carrying out conditional sampling of the wall shear stress data based on a combined threshold magnitude and time-duration criteria. The use of three different scalings (so-called outer, inner and mixed) for the time-duration criterion for the conditional events is explored. It is found that if the time-duration criterion is kept constant in inner units, the frequency of occurrence of these conditional events remain insensitive to Reynolds number. There exists an exponential distribution of frequency of occurrence of the conditional events with respect to their duration, implying a potentially memoryless process. An explanation for the presence of a spike (or dip) in the ensemble-averaged wall shear stress data before and after the low-drag (or high-drag) events is investigated. During the low-drag events, the conditionally-averaged streamwise velocities get closer to Virk’s maximum drag reduction (MDR) asymptote, near the wall, for all Reynolds numbers studied. Reynolds shear stress (RSS) characteristics during these conditional events are investigated for Reτ = 70 and 85. Except very close to the wall, the conditionally-averaged RSS is higher than the time-averaged value during the low-drag events. Full article
(This article belongs to the Special Issue Intermittency in Transitional Shear Flows)
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Article
Flow Statistics in the Transitional Regime of Plane Channel Flow
Entropy 2020, 22(9), 1001; https://doi.org/10.3390/e22091001 - 08 Sep 2020
Cited by 5 | Viewed by 1084
Abstract
The transitional regime of plane channel flow is investigated above the transitional point below which turbulence is not sustained, using direct numerical simulation in large domains. Statistics of laminar-turbulent spatio-temporal intermittency are reported. The geometry of the pattern is first characterized, including statistics [...] Read more.
The transitional regime of plane channel flow is investigated above the transitional point below which turbulence is not sustained, using direct numerical simulation in large domains. Statistics of laminar-turbulent spatio-temporal intermittency are reported. The geometry of the pattern is first characterized, including statistics for the angles of the laminar-turbulent stripes observed in this regime, with a comparison to experiments. High-order statistics of the local and instantaneous bulk velocity, wall shear stress and turbulent kinetic energy are then provided. The distributions of the two former quantities have non-trivial shapes, characterized by a large kurtosis and/or skewness. Interestingly, we observe a strong linear correlation between their kurtosis and their skewness squared, which is usually reported at much higher Reynolds number in the fully turbulent regime. Full article
(This article belongs to the Special Issue Intermittency in Transitional Shear Flows)
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Article
Intermittency and Critical Scaling in Annular Couette Flow
Entropy 2020, 22(9), 988; https://doi.org/10.3390/e22090988 - 04 Sep 2020
Cited by 5 | Viewed by 1799
Abstract
The onset of turbulence in subcritical shear flows is one of the most puzzling manifestations of critical phenomena in fluid dynamics. The present study focuses on the Couette flow inside an infinitely long annular geometry where the inner rod moves with constant velocity [...] Read more.
The onset of turbulence in subcritical shear flows is one of the most puzzling manifestations of critical phenomena in fluid dynamics. The present study focuses on the Couette flow inside an infinitely long annular geometry where the inner rod moves with constant velocity and entrains fluid, by means of direct numerical simulation. Although for a radius ratio close to unity the system is similar to plane Couette flow, a qualitatively novel regime is identified for small radius ratio, featuring no oblique bands. An analysis of finite-size effects is carried out based on an artificial increase of the perimeter. Statistics of the turbulent fraction and of the laminar gap distributions are shown both with and without such confinement effects. For the wider domains, they display a cross-over from exponential to algebraic scaling. The data suggest that the onset of the original regime is consistent with the dynamics of one-dimensional directed percolation at onset, yet with additional frustration due to azimuthal confinement effects. Full article
(This article belongs to the Special Issue Intermittency in Transitional Shear Flows)
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