dorsal/arxiv
View SchemaModel for convection in binary liquids
| Authors | St. Hollinger, M. Luecke, H. W. Mueller |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9805003 |
| URL | https://arxiv.org/abs/patt-sol/9805003 |
| DOI | 10.1103/PhysRevE.57.4250 |
| Journal | Phys. Rev. E 57, 4250 - 4264 (1998) |
Abstract
A minimal, analytically manageable Galerkin type model for convection in binary mixtures subject to realistic boundary conditions is presented. The model elucidates and reproduces the typical bifurcation topology of extended stationary and oscillatory convective states seen for negative Soret coupling: backwards stationary and Hopf bifurcations, saddle node bifurcations to stable strongly nonlinear stationary and traveling wave (TW) states, and merging of the TW solution branch with stationary states. Also unstable standing wave solutions are obtained. A systematic analysis of the concentration balance for liquid mixture parameters has lead to a representation of the concentration field in terms of two linear and two nonlinear modes. This truncation captures the important large--scale effects in the laterally averaged concentration field resulting from advective and diffusive mixing. Also the fact that with increasing flow intensity along the TW solution branch the frequency decreases monotonically in the same way as the mixing increases --- the variance of the concentration distribution decreases --- is ensured and reproduced well. Universal scaling relations between flow intensity, frequency, and variance of the concentration distribution (degree of mixing) in a TW are predicted by the model and have been confirmed by numerical solutions of the full equations. The validity of the model is checked by comparison with numerical solutions of the full field equations.
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"abstract": "A minimal, analytically manageable Galerkin type model for convection in\nbinary mixtures subject to realistic boundary conditions is presented. The\nmodel elucidates and reproduces the typical bifurcation topology of extended\nstationary and oscillatory convective states seen for negative Soret coupling:\nbackwards stationary and Hopf bifurcations, saddle node bifurcations to stable\nstrongly nonlinear stationary and traveling wave (TW) states, and merging of\nthe TW solution branch with stationary states. Also unstable standing wave\nsolutions are obtained. A systematic analysis of the concentration balance for\nliquid mixture parameters has lead to a representation of the concentration\nfield in terms of two linear and two nonlinear modes. This truncation captures\nthe important large--scale effects in the laterally averaged concentration\nfield resulting from advective and diffusive mixing. Also the fact that with\nincreasing flow intensity along the TW solution branch the frequency decreases\nmonotonically in the same way as the mixing increases --- the variance of the\nconcentration distribution decreases --- is ensured and reproduced well.\nUniversal scaling relations between flow intensity, frequency, and variance of\nthe concentration distribution (degree of mixing) in a TW are predicted by the\nmodel and have been confirmed by numerical solutions of the full equations. The\nvalidity of the model is checked by comparison with numerical solutions of the\nfull field equations.",
"arxiv_id": "patt-sol/9805003",
"authors": [
"St. Hollinger",
"M. Luecke",
"H. W. Mueller"
],
"categories": [
"patt-sol",
"nlin.PS"
],
"doi": "10.1103/PhysRevE.57.4250",
"journal_ref": "Phys. Rev. E 57, 4250 - 4264 (1998)",
"title": "Model for convection in binary liquids",
"url": "https://arxiv.org/abs/patt-sol/9805003"
},
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