The Onset of Turbulence in Pipe Flow (original) (raw)
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Turbulence Transition in Pipe Flow
Annual Review of Fluid Mechanics, 2007
Pipe flow is a prominent example among the shear flows that undergo transition to turbulence without mediation by a linear instability of the laminar profile. Experiments on pipe flow, as well as plane Couette and plane Poiseuille flow, show that triggering turbulence depends sensitively on initial conditions, that between the laminar and the turbulent states there exists no intermediate state with simple spatial or temporal characteristics, and that turbulence is not persistent, i.e., it can decay again, if the observation time is long enough. All these features can consistently be explained on the assumption that the turbulent state corresponds to a chaotic saddle in state space. The goal of this review is to explain this concept, summarize the numerical and experimental evidence for pipe flow, and outline the consequences for related flows.
Critical Behaviour in the Relaminarisation of Localised Turbulence in Pipe Flow
2006
The statistics of the relaminarisation of localised turbulence in a pipe are examined by direct numerical simulation. As in recent experimental data (Peixinho & Mullin, Phys. Rev. Lett. 96, 094501, 2006), the half life for the decaying turbulence is consistent with the scaling (Re_c-Re)^{-1}, indicating a boundary crisis of the localised turbulent state familiar in low-dimensional dynamical systems. The crisis Reynolds number, is estimated as Re_c=1870, a value within 7% of the experimental value 1750. We argue that the frequently-asked question of which Re and initial disturbance are needed to trigger sustained turbulence in a pipe, is really two separate questions: the `local phase space' question (local to the laminar state) of what threshold disturbance at a given Re is needed to initially trigger turbulence, followed by the `global phase space' question of whether Re exceeds Re_c at which point the turbulent state becomes an attractor.
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