453 research outputs found
Direct and noisy transitions in a model shear flow
The transition to turbulence in flows where the laminar profile is linearly
stable requires perturbations of finite amplitude. "Optimal" perturbations are
distinguished as extrema of certain functionals, and different functionals give
different optima. We here discuss the phase space structure of a 2-d simplified
model of the transition to turbulence and discuss optimal perturbations with
respect to three criteria: energy of the initial condition, energy dissipation
of the initial condition and amplitude of noise in a stochastic transition. We
find that the states that trigger the transition are different in the three
cases, but show the same scaling with Reynolds number
Sensitive dependence on initial conditions in transition to turbulence in pipe flow
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.Comment: 10 pages, 12 figures; submitted to J. Fluid Mec
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