dorsal/arxiv
View SchemaPhenomenological Theory for Spatiotemporal Chaos in Rayleigh-Benard Convection
| Authors | Xiao-jun Li, Hao-wen Xi, J. D. Gunton |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9706007 |
| URL | https://arxiv.org/abs/patt-sol/9706007 |
Abstract
We present a phenomenological theory for spatiotemporal chaos (STC) in Rayleigh-Benard convection, based on the generalized Swift-Hohenberg model. We apply a random phase approximation to STC and conjecture a scaling form for the structure factor $S(k)$ with respect to the correlation length $\xi_2$. We hence obtain analytical results for the time-averaged convective current $J$ and the time-averaged vorticity current $\Omega$. We also define power-law behaviors such as $J \sim \epsilon^\mu$, $\Omega \sim \epsilon^\lambda$ and $\xi_2 \sim \epsilon^{-\nu}$, where $\epsilon$ is the control parameter. We find from our theory that $\mu = 1$, $\nu \ge 1/2$ and $\lambda = 2 \mu + \nu$ for phase turbulence and that $\mu = 1$, $\nu \ge 1/2$ and $\lambda = 2 \mu + 2 \nu$ for spiral-defect chaos. These predictions, together with the scaling conjecture for $S(k)$, are confirmed by our numerical results. Finally we suggest that Porod's law, $S(k) \sim 1/\xi_2 k^3$ for large $k$, might be valid in STC.
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"date_modified": "2026-03-02T18:00:29.278000Z",
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"abstract": "We present a phenomenological theory for spatiotemporal chaos (STC) in\nRayleigh-Benard convection, based on the generalized Swift-Hohenberg model. We\napply a random phase approximation to STC and conjecture a scaling form for the\nstructure factor $S(k)$ with respect to the correlation length $\\xi_2$. We\nhence obtain analytical results for the time-averaged convective current $J$\nand the time-averaged vorticity current $\\Omega$. We also define power-law\nbehaviors such as $J \\sim \\epsilon^\\mu$, $\\Omega \\sim \\epsilon^\\lambda$ and\n$\\xi_2 \\sim \\epsilon^{-\\nu}$, where $\\epsilon$ is the control parameter. We\nfind from our theory that $\\mu = 1$, $\\nu \\ge 1/2$ and $\\lambda = 2 \\mu + \\nu$\nfor phase turbulence and that $\\mu = 1$, $\\nu \\ge 1/2$ and $\\lambda = 2 \\mu + 2\n\\nu$ for spiral-defect chaos. These predictions, together with the scaling\nconjecture for $S(k)$, are confirmed by our numerical results. Finally we\nsuggest that Porod\u0027s law, $S(k) \\sim 1/\\xi_2 k^3$ for large $k$, might be valid\nin STC.",
"arxiv_id": "patt-sol/9706007",
"authors": [
"Xiao-jun Li",
"Hao-wen Xi",
"J. D. Gunton"
],
"categories": [
"patt-sol",
"chao-dyn",
"cond-mat.stat-mech",
"nlin.CD",
"nlin.PS",
"physics.flu-dyn"
],
"title": "Phenomenological Theory for Spatiotemporal Chaos in Rayleigh-Benard Convection",
"url": "https://arxiv.org/abs/patt-sol/9706007"
},
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"variant": "snapshot-2026-03-01",
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