Subcritical transition to turbulence in plane Couette flow

Daviaud, François; Hegseth, John; Bergé, P.

doi:10.1103/physrevlett.69.2511

Cited by 176 publications

(160 citation statements)

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“…(Here Re UD= , where U is the mean velocity, D is the diameter of the pipe, and is the kinematic viscosity of the fluid.) Similar observations have been made in related shear flows such as Couette [3][4][5], Poiseuille, and boundary layer flows where turbulence sets in despite linear stability [2] or the linear instability mechanism can be bypassed. Understanding the transition scenario and the nature of the resulting turbulent flows is one of the greatest challenges in fluid dynamics.…”

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confidence: 48%

Turbulence Regeneration in Pipe Flow at Moderate Reynolds Numbers

et al. 2005

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We present the results of an experimental investigation into the nature and structure of turbulent pipe flow at moderate Reynolds numbers. A turbulence regeneration mechanism is identified which sustains a symmetric traveling wave within the flow. The periodicity of the mechanism allows comparison to the wavelength of numerically observed exact traveling wave solutions and close agreement is found. The advection speed of the upstream turbulence laminar interface in the experimental flow is observed to form a lower bound on the phase velocities of the exact traveling wave solutions. Overall our observations suggest that the dynamics of the turbulent flow at moderate Reynolds numbers are governed by unstable nonlinear traveling waves. A process which is believed to be of relevance for transition in shear flows is the so called lift-up mechanism [6]. Here streamwise vortices of relatively small magnitude transport low momentum fluid away from the wall and high momentum fluid towards the wall creating strong anomalies in the velocity profile, so-called low-and high-speed streaks (elongated regions of low or high streamwise velocity with respect to their surroundings). During this process the initial perturbation amplitude can grow substantially. Since the mechanism is of a linear nature, in linearly stable flows eventually all perturbations will decay. However it is assumed that once the perturbation has reached a sufficiently large amplitude nonlinear effects will become important and lead to secondary instabilities. The mathematical reason for the transient growth of initial perturbations is the non-normality of the linearized NavierStokes operator and this mechanism has attracted considerable attention [7][8][9].In more recent studies the relevance of nonlinear effects and, in particular, the role of nonlinear solutions has been discussed [10,11]. Such solutions have been calculated for Couette and Poiseuille flow [12 -16] and more recently also for pipe flow [17,18]. These new flow states arise at finite values of the control parameter (Re) and in the case of pipe flow they take the form of traveling waves (TWs), which are coherent flow structures propagating at a constant phase speed in the streamwise direction. Typically these TW solutions are unstable so that the laminar flow state remains the only stable solution. In analogy to observations in low dimensional models [19,20] it has been suggested that as the Reynolds number is increased further the unstable states undergo secondary bifurcations and form an attracting region in phase space which gives rise to turbulent dynamics. The basin of attraction of the turbulent state grows with increasing Reynolds number, so that smaller and smaller perturbations are sufficient to destabilize the laminar flow.Confirmation of this picture has been provided by recent experiments in pipe flow where transients of unstable TWs have been observed that are in close agreement with the numerical solutions [21]. Further experimental investigations have demonstrated that the sta...

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confidence: 48%

Turbulence Regeneration in Pipe Flow at Moderate Reynolds Numbers

et al. 2005

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“…A transition to turbulence via spatio-temporal intermittency has been observed in models of phase equations [1] and coupled map lattices [2] as well as in 1D Rayleigh-Bénard convection [3], in the Printer's instability [4] or in capillary ripples [5]. A similar regime is also observed in circular [6] or plane Couette [7] flows. Spatio-temporal chaos can also appear by an increase of the number of defects as it is seen in Ginzburg Landau equations [8] or in convection in binary fluid mixtures [9].…”

Section: Traveling Waves In a Fluid Layermentioning

confidence: 84%

Traveling waves in a fluid layer subjected to a horizontal temperature gradient

1993

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URL: http://www-spht.cea.fr/articles/S93/017 http://fr.arxiv.org/abs/cond-mat/9303049International audienceWe report experimental observations of traveling waves in a pure fluid with a free surface situated in a long container submitted to a horizontal temperature gradient perpendicular to its large extension. Above a critical value of the gradient and depending on the height of liquid $ h, $ a source of waves is created in the container for small value of $ h, $ while the system exhibits stationary patterns for larger values of $ h. $ The spatio-temporal properties of the waves are studied and compared to theoretical predictions. ----- Ce court article résume les premiers résultats acquis dans cette nouvelle configuration longitudinale: comme dans les travaux précédents des mêmes auteurs, nous sommes dans le cas d'un canal horizontal rempli d'un liquide. Cette fois l'instabilité est provoquée par un gradient horizontal de température. La phénoménologie observée rappelle fortement le cas où le chauffage se fait à l'aide d'un fil conducteur placé sous la surface: un système d'ondes propagatives apparaît dès le seuil de l'instabilité, lequel subit ensuite des bifurcations l'amenant à une dynamique spatiotemporelle non-triviale. En dehors de la nouveauté indiscutable de ces résultats, c'est bien l'analogie avec le cas du fil chaud qui me paraît la plus prometteuse: elle montre la généralité de ces phénomènes, et permet d'espérer une clarification des véritables mécanismes à l'origine de l'instabilité dans un cas comme dans l'autre. Ce travail mérite d'être publié et poursuivi. \vskip 20mm \hfill{Huges Chaté

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“…Fortunately, a family of such flows exists, in the recently-discovered "exact coherent states" (ECS) found by computational bifurcation analysis in plane Couette and plane Poiseuille flows [12,13,14,15,16]. These are three-dimensional, traveling wave flows (hence steady in a traveling reference frame) that appear via saddle-node bifurcations [35] at a Reynolds number somewhat below the transition value seen in experiments [17,18]. The structure of the ECS captures the counter-rotating staggered streamwise vortices that dominate the structure in the buffer region.…”

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confidence: 99%

Toward a Structural Understanding of Turbulent Drag Reduction: Nonlinear Coherent States in Viscoelastic Shear Flows

Stone

Waleffe²,

Graham

2002

Phys. Rev. Lett.

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Nontrivial steady flows have recently been found that capture the main structures of the turbulent buffer layer. We study the effects of polymer addition on these "exact coherent states" (ECS) in plane Couette flow. Despite the simplicity of the ECS flows, these effects closely mirror those observed experimentally: structures shift to larger length scales, wall-normal fluctuations are suppressed while streamwise ones are enhanced, and drag is reduced. The mechanism underlying these effects is elucidated. These results suggest that the ECS are closely related to buffer layer turbulence.PACS numbers: 83.60. Yz,83.80.Rs,47.20.Ky,47.27.Cn Rheological drag reduction, the suppression by additives of skin friction in turbulent flow, has received much attention since its discovery in 1947 [1,2,3]. For many polymer-solvent systems, the pressure drop measured in the pipe flow of the solution can be 30 − 50% less than for the solvent alone. The central rheological feature of drag-reducing additives is their extensional behavior in solution: for dilute polymer solutions in particular the stresses arising in extensional flow can be orders of magnitude larger than those developed in a shear flow. This fact is well-recognized; nevertheless the mechanism of interaction between polymer stretching and turbulent structure is not well-understood and the goal of the present work is to attempt to shed light on this interaction.A key structural observation from experiments and direct numerical simulations (DNS) of drag-reducing solutions is the modification of the buffer region near the wall [4,5,6,7,8,9,10]. It has long been known that the flow in this region is very structured, containing streamwise vortices that lead to streaks in the streamwise velocity [11]; these structures are thickened in both the wall-normal and spanwise directions during flow of drag reducing solutions [4,5]. Because of its importance in the production and dissipation of turbulent energy [11], any effort to mechanistically understand rheological drag reduction should address this region.To better understand the effect of the polymer on the buffer layer, we wish to study a model flow that has structures similar to those seen in this region but without the full complexities of time-dependent turbulent flows. Fortunately, a family of such flows exists, in the recently-discovered "exact coherent states" (ECS) found by computational bifurcation analysis in plane Couette and plane Poiseuille flows [12,13,14,15,16]. These are three-dimensional, traveling wave flows (hence steady in a traveling reference frame) that appear via saddle-node bifurcations [35] at a Reynolds number somewhat below the transition value seen in experiments [17,18]. The structure of the ECS captures the counter-rotating staggered streamwise vortices that dominate the structure in the buffer region. From the dynamical point of view, there is evidence that these states form a part of the dynamical skeleton of the turbulent flow: i.e., they are saddle points that underlie the strange attract...

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Subcritical transition to turbulence in plane Couette flow

Cited by 176 publications

References 20 publications

Turbulence Regeneration in Pipe Flow at Moderate Reynolds Numbers

Turbulence Regeneration in Pipe Flow at Moderate Reynolds Numbers

Traveling waves in a fluid layer subjected to a horizontal temperature gradient

Toward a Structural Understanding of Turbulent Drag Reduction: Nonlinear Coherent States in Viscoelastic Shear Flows

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