New results in rotating Hagen–Poiseuille flow

Barnes, David R.; Kerswell, Rich R.

doi:10.1017/s0022112000008909

Cited by 28 publications

(29 citation statements)

References 35 publications

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“…The existence of exact coherent states in pipe flow has been an object of speculation for some time [7,12,19] but different earlier attempts to find them numerically have failed [3,44].…”

Section: Discussionmentioning

confidence: 99%

“…Barnes & Kerswell [3] investigated in travelling waves in rotating pipe flow where fluid is driven by a constant pressure gradient along a pipe which is rotating axially as well as about a perpendicular diameter, i.e. a rotating and precessing pipe.…”

Section: Earlier Attempts To Find Coherent States In Pipe Flowmentioning

confidence: 99%

“…For a sketch of their bifurcation diagram see Fig. 6.1 (taken from [3], modified). Low axial rotation rates are known to lead to a linear instability of the laminar profile [47] from which nonlinear two-dimensional helical waves emerge [86].…”

Section: Earlier Attempts To Find Coherent States In Pipe Flowmentioning

confidence: 99%

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Turbulence Transition in Pipe Flow

Eckhardt

Schneider

Hof

et al. 2007

Annu. Rev. Fluid Mech.

505

456

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Pipe flow is a prominent example among the shear flows that undergo transition to turbulence without mediation by a linear instability of the laminar profile. Experiments on pipe flow, as well as plane Couette and plane Poiseuille flow, show that triggering turbulence depends sensitively on initial conditions, that between the laminar and the turbulent states there exists no intermediate state with simple spatial or temporal characteristics, and that turbulence is not persistent, i.e., it can decay again, if the observation time is long enough. All these features can consistently be explained on the assumption that the turbulent state corresponds to a chaotic saddle in state space. The goal of this review is to explain this concept, summarize the numerical and experimental evidence for pipe flow, and outline the consequences for related flows.

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“…The existence of exact coherent states in pipe flow has been an object of speculation for some time [7,12,19] but different earlier attempts to find them numerically have failed [3,44].…”

Section: Discussionmentioning

confidence: 99%

Section: Earlier Attempts To Find Coherent States In Pipe Flowmentioning

confidence: 99%

See 1 more Smart Citation

Turbulence Transition in Pipe Flow

Eckhardt

Schneider

Hof

et al. 2007

Annu. Rev. Fluid Mech.

505

456

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“…5 appeared as a plausible alternative to the centrifugal instability approach in order to identify a self-sustaining process at R Ω = −1. Such an attempt was further encouraged by the work of Wedin & Kerswell (2004), who managed to identify a self-sustaining process in non-rotating pipe Poiseuille flow by continuing forced nonlinear solutions, whereas Barnes & Kerswell (2000) had previously been unable to continue nonlinear solutions obtained for a rotating pipe Poiseuille flow down to zero rotation.…”

Section: Pitfalls Of the Forcing Approachmentioning

confidence: 99%

On self-sustaining processes in Rayleigh-stable rotating plane Couette flows and subcritical transition to turbulence in accretion disks

Rincon¹,

Ogilvie²,

Cossu

2006

A&A

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Context. Subcritical transition to turbulence in Keplerian accretion disks is still a controversial issue and some theoretical progress is required in order to determine whether or not this scenario provides a plausible explanation for the origin of angular momentum transport in non-magnetized accretion disks. Aims. Motivated by the recent discoveries of exact nonlinear steady self-sustaining solutions in linearly stable non-rotating shear flows, we attempt to compute similar solutions in Rayleigh-stable rotating plane Couette flows and to identify transition mechanisms in such flows. Methods. Numerical simulations (time-stepping approaches) have been employed in most recent studies of the problem. Here, we instead combine nonlinear continuation methods and asymptotic theory to study the nonlinear dynamics of plane Couette flows in Rayleigh-stable regimes. Results. We obtain exact nonlinear solutions for Rayleigh-stable cyclonic regimes using continuation techniques proposed by Waleffe and Nagata but show that it is not possible to compute solutions for Rayleigh-stable anticyclonic regimes, including Keplerian flow, using similar techniques. We also present asymptotic descriptions of these various problems at large Reynolds numbers that provide some insight into the differences between the non-rotating and Rayleigh-stable anticyclonic regimes and derive some necessary conditions for mechanisms analogous to the non-rotating self-sustaining process to be present in (constant angular momentum) flows on the Rayleigh line.Conclusions. Our results demonstrate that subcritical transition mechanisms cannot be identified in wall-bounded Rayleigh-stable anticyclonic shear flows by transposing directly the phenomenology of subcritical transition in cyclonic and non-rotating wall-bounded shear flows. Asymptotic developments, however, leave open the possibility that nonlinear self-sustaining solutions may exist in unbounded or periodic flows on the Rayleigh line. These could serve as a starting point to discover solutions in Rayleigh-stable flows, but the nonlinear stability of Keplerian accretion disks remains to be determined.

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“…This has been successful in other cases [13,15,16]. For pipe flow Barnes and Kerswell [23] showed that the instabilities that arise from rotation do not extend to the case of pure pipe flow. Guided by the dominance of downstream vortices in the stationary and travelling states in planar shear flows we therefore adopted the following strategy, similar to the one used in [14]: at low Reynolds number a volume force F that generates a transverse flow with translation invariant downstream vortices was added.…”

mentioning

confidence: 97%

Traveling Waves in Pipe Flow

2003

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A family of three-dimensional travelling waves for flow through a pipe of circular cross section is identified. The travelling waves are dominated by pairs of downstream vortices and streaks. They originate in saddle-node bifurcations at Reynolds numbers as low as 1250. All states are immediately unstable. Their dynamical significance is that they provide a skeleton for the formation of a chaotic saddle that can explain the intermittent transition to turbulence and the sensitive dependence on initial conditions in this shear flow.PACS numbers: 47.20.Ft ,47.20.Lz ,47.35.+i Based on decades of studies it is consensus that HagenPoiseuille flow through a pipe of circular cross section belongs to the class of shear flows that does not become linearly unstable. Nevertheless, it undergoes an intermittent transition to turbulence for sufficiently high Reynolds numbers and sufficiently large initial perturbations, as first documented in the classic experiments by Reynolds [1]. Since then many studies have analyzed the mechanisms of transition and the properties of the turbulent state [2,3,4,5,6]. Particularly relevant to the present analysis are the investigations by Darbyshire and Mullin [7] which clearly show a strong sensitivity to perturbations and a broad intermittent range of decaying and turbulent perturbations in an amplitude vs. Reynolds number plane. Experimental and numerical studies [3,8] show that the turbulent flow in the transition region is dominated by downstream vortices and streaks. Various models for their dynamics have been analyzed [9,10]. Taking the full nonlinearity into account Waleffe developed the concept of a nonlinear turbulence cycle for the regeneration of vortices and streaks [11]. In addition, stationary solutions and travelling waves have been found in the full nonlinear equations for plane Couette, Taylor-Couette and plane Poiseuille flow [12,13,14,15,16]. It has been suggested that these structures provide a skeleton for the transition to turbulence and the observed intermittency [17,18]. They clearly dominate various observables in low Reynolds number turbulent flows [10], and are also relevant for an understanding of the effects of non-Newtonian additives [19].The existence of exact coherent states in pipe flow has been an object of speculation for some time [5,6,7]. As we will show here Hagen-Poiseuille flow supports families of travelling waves with structures similar to those observed in other shear flows as well. This underlines the significance of vortex-streak interactions also in this system and opens alternative routes to modelling and controlling pipe flow. * Electronic address: Holger.Faisst@physik.uni-marburg.deThe existence of stationary states in plane Couette flow is connected with an inversion symmetry in the laminar profile. In the absence of such a symmetry in pipe flow the simplest states we can expect are travelling waves (TWs), i.e. coherent structures that move with constant wave speed. The wave speed depends on shape and structure and is not known in advance....

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New results in rotating Hagen–Poiseuille flow

Cited by 28 publications

References 35 publications

Turbulence Transition in Pipe Flow

Turbulence Transition in Pipe Flow

On self-sustaining processes in Rayleigh-stable rotating plane Couette flows and subcritical transition to turbulence in accretion disks

Traveling Waves in Pipe Flow

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