Modeling transitional plane Couette flow

Lagha, Maher; Manneville, Paul

doi:10.1140/epjb/e2007-00243-y

Cited by 44 publications

(65 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This indicates that for long times the decay of turbulence is a Poisson process, which is a hallmark of a chaotic repeller [7,8]. The same behavior has been reported in all previous studies of the decay of turbulence in plane Couette and pipe flows [5,6,10,12,13,14,15]. τ was calculated by fitting a straight line to the tail of each distribution.…”

supporting

confidence: 73%

“…Above Re c the dynamics of the turbulent state are typically associated with those of a chaotic attractor [11]. Other experiments and simulations suggest that characteristic lifetimes do not diverge, instead increasing very rapidly but remaining finite at finite Re [12,13,14,15]. This implies that turbulence is not a permanent state of the flow for any Re and is instead generically transient, if very long-lived.…”

mentioning

confidence: 98%

See 1 more Smart Citation

Transient turbulence in Taylor-Couette flow

2010

View full text Add to dashboard Cite

Recent studies have brought into question the view that at sufficiently high Reynolds number turbulence is an asymptotic state. We present the first direct observation of the decay of turbulent states in Taylor-Couette flow with lifetimes spanning five orders of magnitude. We also show that there is a regime where Taylor-Couette flow shares many of the decay characteristics observed in other shear flows, including Poisson statistics and the coexistence of laminar and turbulent patches. Our data suggest that characteristic decay times increase super-exponentially with increasing Reynolds number but remain bounded in agreement with the most recent data from pipe flow and with a recent theoretical model. This suggests that, contrary to the prevailing view, turbulence in linearly stable shear flows may be generically transient.

show abstract

supporting

confidence: 73%

mentioning

confidence: 98%

Transient turbulence in Taylor-Couette flow

2010

View full text Add to dashboard Cite

show abstract

“…A system of partial differential equations was derived by means of standard Galerkin expansion/projection of the Navier-Stokes equations, using a polynomial basis appropriate to no-slip boundary conditions; see [24] for a full description and details on its numerical implementation. This system extends Waleffe's model [4] by unfreezing the in-plane spatial dependence of the velocity field while keeping a few wall-normal modes.…”

mentioning

confidence: 99%

Spatiotemporal perspective on the decay of turbulence in wall-bounded flows

Manneville

2009

Phys. Rev. E

View full text Add to dashboard Cite

Using a reduced model focusing on the in-plane dependence of plane Couette flow, it is shown that the turbulent → laminar relaxation process can be understood as a nucleation problem similar to that occurring at a thermodynamic first-order phase transition. The approach, apt to deal with the large extension of the system considered, challenges the current interpretation in terms of chaotic transients typical of temporal chaos. The study of the distribution of the sizes of laminar domains embedded in turbulent flow proves that an abrupt transition from sustained spatiotemporal chaos to laminar flow can take place at some given value of the Reynolds number R low , whether or not the local chaos lifetime, as envisioned within low-dimensional dynamical systems theory, diverges at finite R beyond R low . PACS: 47.20.Ft, 47.27.Cn, 05.45.Jn The transition to turbulence in flows lacking linear instability modes, such as Poiseuille pipe flow driven by a pressure gradient along a circular tube (Ppf) and plane Couette flow driven by two plates moving parallel to each other in opposite directions (pCf), is particularly delicate to understand owing to its abrupt character, without the usual cascade seen in the globally super-critical case, as for e.g. convection. A recent general presentation of the issues is given in [1]. These globally sub-critical flows become turbulent through the nucleation and growth or decay of turbulent domains called puffs (Ppf) or spots (pCf), see, e.g., [2] and [3] for Ppf and pCf, respectively. Most of the work on the transition problem has dealt with special nonlinear solutions (exact coherent structures [4, b]) to the Navier-Stokes equations and their dynamics in the phase space spanned by them. Such solutions, obtained within the so-called Minimal Flow Unit (MFU) assumption [5], have been found at moderate values of the Reynolds number R in Ppf, [6], pCf [4,[7][8][9], and also in plane Poiseuille flow [8,10]. (In pCf, R is defined as Uh/ν where U is the speed of the plates driving the flow, 2h the gap petween the plates, and ν the kinematic viscosity of the fluid.) These solutions are all unstable and, together with their stable and unstable manifolds, they form the skeleton of the turbulent flow at a local scale. The reason why turbulence can be sustained only at much higher values of R (about a factor of two to three higher) is however not clear [2].

show abstract

“…Stress-free boundary conditions allow the use of trigonometric functions [69] that greatly ease the exact analytical treatment and the subsequent work-load reduction [55,70], but this reduced description is not limited to the stress-free case: comparable results can also obtained in the no-slip case with adapted basis functions [72][73][74], or for possibly other systems in the same class. The no-slip approach is more cumbersome, but has the merit to make the structure of the resulting model explicit, and to point out that specificities of the problem only lie in the precise values of the coefficients in the general model [73].…”

Section: Plane Couette Flowmentioning

confidence: 99%

Laminar-Turbulent Patterning in Transitional Flows

Manneville

2017

Entropy

View full text Add to dashboard Cite

Wall-bounded flows experience a transition to turbulence characterized by the coexistence of laminar and turbulent domains in some range of Reynolds number R, the natural control parameter. This transitional regime takes place between an upper threshold R t above which turbulence is uniform (featureless) and a lower threshold R g below which any form of turbulence decays, possibly at the end of overlong chaotic transients. The most emblematic cases of flow along flat plates transiting to/from turbulence according to this scenario are reviewed. The coexistence is generally in the form of bands, alternatively laminar and turbulent, and oriented obliquely with respect to the general flow direction. The final decay of the bands at R g points to the relevance of directed percolation and criticality in the sense of statistical-physics phase transitions. The nature of the transition at R t where bands form is still somewhat mysterious and does not easily fit the scheme holding for pattern-forming instabilities at increasing control parameter on a laminar background. In contrast, the bands arise at R t out of a uniform turbulent background at a decreasing control parameter. Ingredients of a possible theory of laminar-turbulent patterning are discussed.Keywords: transition to/from turbulence; wall-bounded shear flow; plane Couette flow; turbulent patterning; phase transitions; directed percolationThe present Special-Issue contribution deals with the transition to turbulence in wall-bounded flows, an important case of systems driven far from equilibrium where patterns develop against a turbulent background. This active field of research is rapidly evolving, and important results have been obtained recently. To set the frame, in Section 1, I will summarize a recent paper reviewing the subject from a more general standpoint [1], enabling me to focus on a specific feature of this transition: the existence of a statistically well-organized laminar-turbulent patterning of flows along planar walls in some intermediate range of Reynolds numbers [R g , R t ]. The Reynolds number is the main control parameter of the problem. Its generic expression reads R = V /ν, in which V and are typical velocity and length scales, and ν the fluid's kinematic viscosity. R compares the typical shear rate V/ to the viscous diffusion rate over the same length scale ν/ 2 . R g is a global stability threshold marking unconditional return to laminar flow and R t some upper threshold beyond which turbulence is essentially uniform. After having taken the cylindrical shear configuration as an illustrating case in Section 2, I will turn to strictly planar cases in Section 3. The best understood part of the transition scenario, pattern decay at R g is considered in Section 4. How patterns emerge as R is decreased from large values is next examined in Section 5 before a discussion of perspectives and questions that, in my view, remain open in Section 6. I have tried to limit the bibliography to contributions of specific significance, historical or...

show abstract

Modeling transitional plane Couette flow

Cited by 44 publications

References 39 publications

Transient turbulence in Taylor-Couette flow

Transient turbulence in Taylor-Couette flow

Spatiotemporal perspective on the decay of turbulence in wall-bounded flows

Laminar-Turbulent Patterning in Transitional Flows

Contact Info

Product

Resources

About