dorsal/arxiv
View SchemaSensitive dependence on initial conditions in transition to turbulence in pipe flow
| Authors | Holger Faisst, Bruno Eckhardt |
|---|---|
| Categories | |
| ArXiv ID | physics/0312078 |
| URL | https://arxiv.org/abs/physics/0312078 |
| DOI | 10.1017/S0022112004008134 |
Abstract
The experiments by Darbyshire and Mullin (J. Fluid Mech. 289, 83 (1995)) on the transition to turbulence in pipe flow show that there is no sharp border between initial conditions that trigger turbulence and those that do not. We here relate this behaviour to the possibility that the transition to turbulence is connected with the formation of a chaotic saddle in the phase space of the system. We quantify a sensitive dependence on initial conditions and find in a statistical analysis that in the transition region the distribution of turbulent lifetimes follows an exponential law. The characteristic mean lifetime of the distribution increases rapidly with Reynolds number and becomes inaccessibly large for Reynolds numbers exceeding about 2200. Suitable experiments to further probe this concept are proposed.
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"abstract": "The experiments by Darbyshire and Mullin (J. Fluid Mech. 289, 83 (1995)) on\nthe transition to turbulence in pipe flow show that there is no sharp border\nbetween initial conditions that trigger turbulence and those that do not. We\nhere relate this behaviour to the possibility that the transition to turbulence\nis connected with the formation of a chaotic saddle in the phase space of the\nsystem. We quantify a sensitive dependence on initial conditions and find in a\nstatistical analysis that in the transition region the distribution of\nturbulent lifetimes follows an exponential law. The characteristic mean\nlifetime of the distribution increases rapidly with Reynolds number and becomes\ninaccessibly large for Reynolds numbers exceeding about 2200. Suitable\nexperiments to further probe this concept are proposed.",
"arxiv_id": "physics/0312078",
"authors": [
"Holger Faisst",
"Bruno Eckhardt"
],
"categories": [
"physics.flu-dyn",
"nlin.CD"
],
"doi": "10.1017/S0022112004008134",
"title": "Sensitive dependence on initial conditions in transition to turbulence in pipe flow",
"url": "https://arxiv.org/abs/physics/0312078"
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