dorsal/arxiv
View SchemaRecurrence of Travelling Waves in Transitional Pipe Flow
| Authors | R. R. Kerswell, O. R. Tutty |
|---|---|
| Categories | |
| ArXiv ID | physics/0611009 |
| URL | https://arxiv.org/abs/physics/0611009 |
| DOI | 10.1017/S0022112007006301 |
Abstract
The recent theoretical discovery of families of travelling wave solutions in pipe flow at Reynolds numbers lower than the transitional range naturally raises the question of their relevance to the turbulent transition process. Here a series of numerical experiments are conducted in which we look for the spatial signature of these travelling waves in transitionary flows. Working within a periodic pipe of 5D (diameters) length, we find that travelling waves with low wall shear stresses (lower branch solutions) are on a surface which separates initial conditions which uneventfully relaminarise and those which lead to a turbulent evolution. Evidence for recurrent travelling wave visits is found in both 5D and 10D long periodic pipes but only for those travelling waves with low-to-intermediate wall shear stress and for less than about 10% of the time in turbulent flow. Given this, it seems unlikely that the mean turbulent properties such as wall shear stress can be predicted as an expansion over the travelling waves in which their individual properties are appropriately weighted. Rather, further dynamical structures such as periodic orbits need to be isolated and included in any such expansion.
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"abstract": "The recent theoretical discovery of families of travelling wave solutions in\npipe flow at Reynolds numbers lower than the transitional range naturally\nraises the question of their relevance to the turbulent transition process.\nHere a series of numerical experiments are conducted in which we look for the\nspatial signature of these travelling waves in transitionary flows. Working\nwithin a periodic pipe of 5D (diameters) length, we find that travelling waves\nwith low wall shear stresses (lower branch solutions) are on a surface which\nseparates initial conditions which uneventfully relaminarise and those which\nlead to a turbulent evolution. Evidence for recurrent travelling wave visits is\nfound in both 5D and 10D long periodic pipes but only for those travelling\nwaves with low-to-intermediate wall shear stress and for less than about 10% of\nthe time in turbulent flow. Given this, it seems unlikely that the mean\nturbulent properties such as wall shear stress can be predicted as an expansion\nover the travelling waves in which their individual properties are\nappropriately weighted. Rather, further dynamical structures such as periodic\norbits need to be isolated and included in any such expansion.",
"arxiv_id": "physics/0611009",
"authors": [
"R. R. Kerswell",
"O. R. Tutty"
],
"categories": [
"physics.flu-dyn"
],
"doi": "10.1017/S0022112007006301",
"title": "Recurrence of Travelling Waves in Transitional Pipe Flow",
"url": "https://arxiv.org/abs/physics/0611009"
},
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