Critical Behaviour in the Relaminarisation of Localised Turbulence in Pipe Flow

Details Critical Behaviour in the Relaminarisation of Localised Turbulence in Pipe Flow Critical Behaviour in the Relaminarisation of Localised Turbulence in Pipe Flow

2006-08-30

arxiv.org/abs/physics/0608292v1

Physics

Fluid Dynamics

4 pages, 6 figures

Scientific paper

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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