dorsal/arxiv
View SchemaPattern formation during Rayleigh-B\'enard convection in non-Boussinesq fluids
| Authors | Hao-wen Xi, J. D. Gunton, Jorge Vinals |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9305001 |
| URL | https://arxiv.org/abs/patt-sol/9305001 |
Abstract
Motivated by recent experimental studies of Bodenschatz et al. [E. Bodenschatz, J.R. de Bruyn, G. Ahlers and D.S. Cannell, Phys. Rev. Lett. {\bf 67}, 3078 (1991) ], we present a numerical study of a generalized two dimensional Swift-Hohenberg equation to model pattern formation in Rayleigh-B\'enard convection in a non-Boussinesq fluid. It is shown that many of the features observed in these experiments can be reproduced by this generalized model that explicitly includes non-Boussinesq and mean flow effects. The spontaneous formation of hexagons, rolls, and a rotating spiral pattern is studied, as well as the transitions and competition among them. Mean flow, non-Boussinesq effects, the geometric shape of the lateral wall, and sidewall forcing are all shown to be crucial in the formation of the rotating spirals. We also study nucleation and growth of hexagonal patterns and find that the front velocity in this two dimensional model is consistent with the prediction of marginal stability theory for one dimensional fronts.
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"abstract": "Motivated by recent experimental studies of Bodenschatz et al. [E.\nBodenschatz, J.R. de Bruyn, G. Ahlers and D.S. Cannell, Phys. Rev. Lett. {\\bf\n67}, 3078 (1991) ], we present a numerical study of a generalized two\ndimensional Swift-Hohenberg equation to model pattern formation in\nRayleigh-B\\\u0027enard convection in a non-Boussinesq fluid. It is shown that many\nof the features observed in these experiments can be reproduced by this\ngeneralized model that explicitly includes non-Boussinesq and mean flow\neffects. The spontaneous formation of hexagons, rolls, and a rotating spiral\npattern is studied, as well as the transitions and competition among them. Mean\nflow, non-Boussinesq effects, the geometric shape of the lateral wall, and\nsidewall forcing are all shown to be crucial in the formation of the rotating\nspirals. We also study nucleation and growth of hexagonal patterns and find\nthat the front velocity in this two dimensional model is consistent with the\nprediction of marginal stability theory for one dimensional fronts.",
"arxiv_id": "patt-sol/9305001",
"authors": [
"Hao-wen Xi",
"J. D. Gunton",
"Jorge Vinals"
],
"categories": [
"patt-sol",
"nlin.PS"
],
"title": "Pattern formation during Rayleigh-B\\\u0027enard convection in non-Boussinesq fluids",
"url": "https://arxiv.org/abs/patt-sol/9305001"
},
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