# zbMATH — the first resource for mathematics

Edge states intermediate between laminar and turbulent dynamics in pipe flow. (English) Zbl 1221.76097
Summary: We studied the dynamics near the boundary between laminar and turbulent dynamics in pipe flow. This boundary contains invariant dynamical states that are attracting when the dynamics is confined to the boundary. These states can be found by controlling a single quantity, in our case the energy content. The edge state is dominated by two downstream vortices and shows intrinsic chaotic dynamics. With increasing Reynolds number the separation between the edge state and turbulence increases. We can track it down to $$Re = 1900$$, where the turbulent lifetimes are short enough that spontaneous decay can also be seen in experiments.

##### MSC:
 76F06 Transition to turbulence 76D05 Navier-Stokes equations for incompressible viscous fluids
##### Keywords:
turbulence transition; pipe flow; coherent states
Full Text:
##### References:
 [1] Z NATURFORSCH 43a pp 697– (1988) [2] J FLUID MECHANICS 289 pp 83– (1995) [3] J FLUID MECHANICS 504 pp 343– (2004) [4] Grossmann, Reviews of Modern Physics 72 (2) pp 603– (2000) · doi:10.1103/RevModPhys.72.603 [5] J FLUID MECHANICS 287 pp 317– (1995) [6] Physical Review Letters 91 pp 244 502– (2003) · doi:10.1103/PhysRevLett.91.244502 [7] Hof, Nature; Physical Science (London) 443 (7107) pp 59– (2006) · doi:10.1038/nature05089 [8] PHIL TRANS R SOC A 367 pp 545– (2009) [9] Physical Review Letters 99 pp 074 502– (2007) · doi:10.1103/PhysRevLett.99.074502 [10] Reynolds, Philosophical Transactions of the Royal Society of London 174 (0) pp 935– (1883) · JFM 16.0845.02 · doi:10.1098/rstl.1883.0029 [11] Chaos (Woodbury, N.Y.) 16 pp 041 103– (2006) · Zbl 05359818 · doi:10.1063/1.2390553 [12] PHYS REV E 75 pp 066 313– (2007) · doi:10.1103/PhysRevE.75.066313 [13] Physical Review Letters 99 pp 034 502– (2007) · doi:10.1103/PhysRevLett.99.034502 [14] Physical Review Letters 96 pp 174 101– (2006) · doi:10.1103/PhysRevLett.96.174101 [15] PHIL TRANS R SOC A 367 pp 561– (2009) [16] PHYS FLUIDS 7 pp 3060– (1995) [17] PHYS FLUIDS 8 pp 2923– (1996)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.