Sensitive dependence on initial conditions in transition to turbulence in pipe flow

被引:145
作者
Faisst, H [1 ]
Eckhardt, B [1 ]
机构
[1] Univ Marburg, Fachbereich Phys, D-35032 Marburg, Germany
关键词
D O I
10.1017/S0022112004008134
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
The experiments by Darbyshire & Mullin (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 2250. Suitable experiments to further probe this concept are proposed.
引用
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页码:343 / 352
页数:10
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