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

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

2003-12-11

arxiv.org/abs/physics/0312078v2

Physics

Fluid Dynamics

10 pages, 12 figures; submitted to J. Fluid Mech

Scientific paper

10.1017/S0022112004008134

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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