dorsal/arxiv
View SchemaCritical Behaviour in the Relaminarisation of Localised Turbulence in Pipe Flow
| Authors | A. P. Willis, R. R. Kerswell |
|---|---|
| Categories | |
| ArXiv ID | physics/0608292 |
| URL | https://arxiv.org/abs/physics/0608292 |
Abstract
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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"abstract": "The statistics of the relaminarisation of localised turbulence in a pipe are\nexamined by direct numerical simulation. As in recent experimental data\n(Peixinho \u0026 Mullin, Phys. Rev. Lett. 96, 094501, 2006), the half life for the\ndecaying turbulence is consistent with the scaling (Re_c-Re)^{-1}, indicating a\nboundary crisis of the localised turbulent state familiar in low-dimensional\ndynamical systems. The crisis Reynolds number, is estimated as Re_c=1870, a\nvalue within 7% of the experimental value 1750. We argue that the\nfrequently-asked question of which Re and initial disturbance are needed to\ntrigger sustained turbulence in a pipe, is really two separate questions: the\n`local phase space\u0027 question (local to the laminar state) of what threshold\ndisturbance at a given Re is needed to initially trigger turbulence, followed\nby the `global phase space\u0027 question of whether Re exceeds Re_c at which point\nthe turbulent state becomes an attractor.",
"arxiv_id": "physics/0608292",
"authors": [
"A. P. Willis",
"R. R. Kerswell"
],
"categories": [
"physics.flu-dyn"
],
"title": "Critical Behaviour in the Relaminarisation of Localised Turbulence in Pipe Flow",
"url": "https://arxiv.org/abs/physics/0608292"
},
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