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

By Holger Faisst, Bruno Eckhardt. Journal of Fluid Mechanics, 2003

185 citations recorded by the source corpus.

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.

Subfields: Computational Mechanics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8fd7e99c2f2dd1aa583dc8024c52ce2d1ba23fe8

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Citations in the corpus

Transition in pipe flow: the saddle structure on the boundary of turbulence (2007, background): “Σ is thought to be of codimension 1 in phase space but one can a priori not exclude a more complex fractal structure, as suggested by the dependence of lifetime on initial conditions in simulations of pipe flow (Faisst & Eckhardt 2004).”
On the relevance of subcritical hydrodynamic turbulence to accretion disk transport (2005, background): “This has been documented both experimentally (Darbyshire & Mullin 1995) and numerically (Faisst & Eckhardt 2004) in pipe flows, and guides to some extent our choice of initial conditions and our numerical procedure.”
Turbulence transition in pipe flow (2007, background): “Of these, a Lyapunov exponent has only been determined in numerical simulations (Faisst & Eckhardt 2004) as it requires a comparison of the time evolution of two states starting from nearby initial conditions–a feat not yet achieved in experimental studies.”
Theoretical perspective on the route to turbulence in a pipe (2016, background): “(See Waleffe (1997), Faisst & Eckhardt (2003), Wedin & Kerswell (2004), Eckhardt et al. (2007), Kawahara, Uhlmann & van Veen (2012) for details of the coherent structures of wall-bounded turbulence, structures that will be here treated as microscopic.”