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

Published online by Cambridge University Press:  16 April 2004

HOLGER FAISST
Affiliation:
Fachbereich Physik, Philipps-Universität Marburg, D-35032 Marburg, Germany
BRUNO ECKHARDT
Affiliation:
Fachbereich Physik, Philipps-Universität Marburg, D-35032 Marburg, Germany

Abstract

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.

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Papers
Copyright
© 2004 Cambridge University Press

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