dorsal/arxiv
View SchemaThreshold amplitudes for transition to turbulence in a pipe
| Authors | Lloyd N. Trefethen, S. J. Chapman, Dan S. Henningson, Alvaro Meseguer, Tom Mullin, F. T. M Nieuwstadt |
|---|---|
| Categories | |
| ArXiv ID | physics/0007092 |
| URL | https://arxiv.org/abs/physics/0007092 |
Abstract
Although flow in a circular pipe is stable to infinitesimal perturbations, it can be excited to turbulence by finite perturbations whose minimal amplitude shrinks as R goes to infinity (R = Reynolds number). Laboratory experiments have appeared to disagree with one another and with theoretical predictions about the dependence of this minimal amplitude on $R$, with published results ranging approximately from $R^{-1/4}$ to $R^{-3/2}$. Here it is shown that these discrepancies can be explained by the use of different definitions of amplitude by different authors. An attempt is made to convert the existing results to a uniform definition of amplitude, the nondimensionalized $L^2$ definition common in the theoretical literature. Although subtleties in the physics raise some questions, agreement appears to be reached on a minimal amplitude that scales as $R^{-3/2 \pm 0.3}$.
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"abstract": "Although flow in a circular pipe is stable to infinitesimal perturbations, it\ncan be excited to turbulence by finite perturbations whose minimal amplitude\nshrinks as R goes to infinity (R = Reynolds number). Laboratory experiments\nhave appeared to disagree with one another and with theoretical predictions\nabout the dependence of this minimal amplitude on $R$, with published results\nranging approximately from $R^{-1/4}$ to $R^{-3/2}$. Here it is shown that\nthese discrepancies can be explained by the use of different definitions of\namplitude by different authors. An attempt is made to convert the existing\nresults to a uniform definition of amplitude, the nondimensionalized $L^2$\ndefinition common in the theoretical literature. Although subtleties in the\nphysics raise some questions, agreement appears to be reached on a minimal\namplitude that scales as $R^{-3/2 \\pm 0.3}$.",
"arxiv_id": "physics/0007092",
"authors": [
"Lloyd N. Trefethen",
"S. J. Chapman",
"Dan S. Henningson",
"Alvaro Meseguer",
"Tom Mullin",
"F. T. M Nieuwstadt"
],
"categories": [
"physics.flu-dyn",
"physics.comp-ph"
],
"title": "Threshold amplitudes for transition to turbulence in a pipe",
"url": "https://arxiv.org/abs/physics/0007092"
},
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