New upper bounds and reduced dynamical modeling for Rayleigh–Bénard convection in a fluid saturated porous layer
► New rigorous upper bounds on the enhancement of heat transport by convection in a porous medium. ► Results are applied to the development of finite dimensional dynamical systems models. ► The number of degrees of freedom in the full dynamics and faithful reduced descriptions are estimated. New rig...
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| Published in | Communications in nonlinear science & numerical simulation Vol. 17; no. 5; pp. 2191 - 2199 |
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| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
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Elsevier B.V
01.05.2012
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| Abstract | ► New rigorous upper bounds on the enhancement of heat transport by convection in a porous medium. ► Results are applied to the development of finite dimensional dynamical systems models. ► The number of degrees of freedom in the full dynamics and faithful reduced descriptions are estimated.
New rigorous upper bounds on the enhancement of heat transport in a fundamental model of porous medium convection are presented. The computational results are applied to the development of finite dimensional dynamical systems models of porous medium convection. The number of degrees of freedom in the full dynamics and the dimension of potentially faithful reduced descriptions are discussed. |
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| AbstractList | New rigorous upper bounds on the enhancement of heat transport in a fundamental model of porous medium convection are presented. The computational results are applied to the development of finite dimensional dynamical systems models of porous medium convection. The number of degrees of freedom in the full dynamics and the dimension of potentially faithful reduced descriptions are discussed. ► New rigorous upper bounds on the enhancement of heat transport by convection in a porous medium. ► Results are applied to the development of finite dimensional dynamical systems models. ► The number of degrees of freedom in the full dynamics and faithful reduced descriptions are estimated. New rigorous upper bounds on the enhancement of heat transport in a fundamental model of porous medium convection are presented. The computational results are applied to the development of finite dimensional dynamical systems models of porous medium convection. The number of degrees of freedom in the full dynamics and the dimension of potentially faithful reduced descriptions are discussed. |
| Author | Dianati, Navid Lunasin, Evelyn Doering, Charles R. Wen, Baole Chini, Gregory P. |
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| Cites_doi | 10.1017/S0022112003007298 10.1017/S0022112073001308 10.1002/mma.478 10.1017/S0022112063001427 10.1017/S0022112094004386 10.1017/S0022112095000978 10.1017/S0022112091002033 10.1007/BF00046977 10.1017/S0022112072000850 10.1016/S0167-2789(99)00165-7 10.1017/S002211209800281X 10.1016/j.physd.2010.06.010 10.5802/afst.666 10.1103/PhysRevLett.59.2911 |
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| Keywords | Number of degrees of freedom Low-dimensional dynamical reduction Stability Convection Porous medium |
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| References | Fabrie (b0040) 1990; 311 Gupta, Joseph (b0050) 1973; 57 Doering, Constantin (b0015) 1998; 376 Chini, Dianati, Zhang, Doering (b0010) 2011; 240 Hamilton, Kim, Waleffe (b0055) 1995; 287 Fabrie (b0035) 1989 Otero, Dontcheva, Johnston, Worthing, Kurganov, Petrova (b0080) 2004; 500 Howard (b0065) 1963; 17 Efendiev, Fuhrmann, Zelik (b0025) 2004; 27 Jiménez, Moin (b0070) 1991; 225 Fabrie (b0030) 1986; 7 Holmes, Lumley, Berkooz (b0060) 1996 Busse, Joseph (b0005) 1972; 54 Robinson (b0085) 2001 Doering, Gibbon, Holm, Nicolaenko (b0020) 1987; 59 Vitanov (b0095) 2000; 136 Graham, Steen (b0045) 1991; 272 Joseph (b0075) 1976 Temam (b0090) 1997 Vitanov (10.1016/j.cnsns.2011.06.039_b0095) 2000; 136 Fabrie (10.1016/j.cnsns.2011.06.039_b0035) 1989 Graham (10.1016/j.cnsns.2011.06.039_b0045) 1991; 272 Busse (10.1016/j.cnsns.2011.06.039_b0005) 1972; 54 Temam (10.1016/j.cnsns.2011.06.039_b0090) 1997 Doering (10.1016/j.cnsns.2011.06.039_b0015) 1998; 376 Jiménez (10.1016/j.cnsns.2011.06.039_b0070) 1991; 225 Gupta (10.1016/j.cnsns.2011.06.039_b0050) 1973; 57 Fabrie (10.1016/j.cnsns.2011.06.039_b0040) 1990; 311 Robinson (10.1016/j.cnsns.2011.06.039_b0085) 2001 Chini (10.1016/j.cnsns.2011.06.039_b0010) 2011; 240 Doering (10.1016/j.cnsns.2011.06.039_b0020) 1987; 59 Otero (10.1016/j.cnsns.2011.06.039_b0080) 2004; 500 Joseph (10.1016/j.cnsns.2011.06.039_b0075) 1976 Efendiev (10.1016/j.cnsns.2011.06.039_b0025) 2004; 27 Hamilton (10.1016/j.cnsns.2011.06.039_b0055) 1995; 287 Fabrie (10.1016/j.cnsns.2011.06.039_b0030) 1986; 7 Howard (10.1016/j.cnsns.2011.06.039_b0065) 1963; 17 Holmes (10.1016/j.cnsns.2011.06.039_b0060) 1996 |
| References_xml | – volume: 54 start-page: 521 year: 1972 end-page: 543 ident: b0005 article-title: Bounds for heat transport in a porous layer publication-title: J Fluid Mech contributor: fullname: Joseph – volume: 500 start-page: 263 year: 2004 end-page: 281 ident: b0080 article-title: High-Rayleigh-number convection in a fluid-saturated porous layer publication-title: J Fluid Mech contributor: fullname: Petrova – volume: 376 start-page: 263 year: 1998 end-page: 296 ident: b0015 article-title: Bounds for heat transport in a porous layer publication-title: J Fluid Mech contributor: fullname: Constantin – volume: 311 start-page: 407 year: 1990 end-page: 410 ident: b0040 article-title: Attracteurs pour deux modèles de convection naturelle en milieux poreux publication-title: CR Acad Sci Paris Sér I Math contributor: fullname: Fabrie – volume: 272 start-page: 67 year: 1991 end-page: 89 ident: b0045 article-title: Plume formation and resonant bifurcations in porous-media convection publication-title: J Fluid Mech contributor: fullname: Steen – volume: 59 start-page: 2911 year: 1987 end-page: 2914 ident: b0020 article-title: Exact Lyapunov dimension of the universal attractor for the complex Ginzburg–Landau equation publication-title: Phys Rev Lett contributor: fullname: Nicolaenko – year: 1976 ident: b0075 article-title: Stability of Fluid Motions. 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1963 end-page: 432 ident: b0065 article-title: Heat transport by turbulent convection publication-title: J Fluid Mech contributor: fullname: Howard – year: 1996 ident: b0060 article-title: Turbulence, Coherent Structures, Dynamical Systems and Symmetry contributor: fullname: Berkooz – volume: 500 start-page: 263 year: 2004 ident: 10.1016/j.cnsns.2011.06.039_b0080 article-title: High-Rayleigh-number convection in a fluid-saturated porous layer publication-title: J Fluid Mech doi: 10.1017/S0022112003007298 contributor: fullname: Otero – year: 1976 ident: 10.1016/j.cnsns.2011.06.039_b0075 contributor: fullname: Joseph – volume: 57 start-page: 491 year: 1973 ident: 10.1016/j.cnsns.2011.06.039_b0050 article-title: Bounds for heat transport in a porous layer publication-title: J Fluid Mech doi: 10.1017/S0022112073001308 contributor: fullname: Gupta – year: 1996 ident: 10.1016/j.cnsns.2011.06.039_b0060 contributor: fullname: Holmes – volume: 27 start-page: 907 year: 2004 ident: 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10.1016/j.cnsns.2011.06.039_b0090 contributor: fullname: Temam – year: 2001 ident: 10.1016/j.cnsns.2011.06.039_b0085 contributor: fullname: Robinson – volume: 287 start-page: 317 year: 1995 ident: 10.1016/j.cnsns.2011.06.039_b0055 article-title: Regeneration mechanisms of near-wall turbulence structures publication-title: J Fluid Mech doi: 10.1017/S0022112095000978 contributor: fullname: Hamilton – volume: 225 start-page: 213 year: 1991 ident: 10.1016/j.cnsns.2011.06.039_b0070 article-title: The minimal flow unit in near-wall turbulence publication-title: J Fluid Mech doi: 10.1017/S0022112091002033 contributor: fullname: Jiménez – volume: 7 start-page: 49 year: 1986 ident: 10.1016/j.cnsns.2011.06.039_b0030 article-title: Solutions fortes et comportement asymptotique pour un modle de convection naturelle en milieu poreux publication-title: Acta Appl Math doi: 10.1007/BF00046977 contributor: fullname: Fabrie – volume: 54 start-page: 521 year: 1972 ident: 10.1016/j.cnsns.2011.06.039_b0005 article-title: Bounds for heat transport in a porous layer publication-title: J Fluid Mech doi: 10.1017/S0022112072000850 contributor: fullname: Busse – volume: 136 start-page: 322 year: 2000 ident: 10.1016/j.cnsns.2011.06.039_b0095 article-title: Upper bounds on the heat transport in a porous layer publication-title: Physica D doi: 10.1016/S0167-2789(99)00165-7 contributor: fullname: Vitanov – volume: 376 start-page: 263 year: 1998 ident: 10.1016/j.cnsns.2011.06.039_b0015 article-title: Bounds for heat transport in a porous layer publication-title: J Fluid Mech doi: 10.1017/S002211209800281X contributor: fullname: Doering – volume: 240 start-page: 241 year: 2011 ident: 10.1016/j.cnsns.2011.06.039_b0010 article-title: Low dimensional models from upper bound theory publication-title: Physica D doi: 10.1016/j.physd.2010.06.010 contributor: fullname: Chini – start-page: 7 issue: 5 1 year: 1989 ident: 10.1016/j.cnsns.2011.06.039_b0035 article-title: Solutions fortes et majorations asymptotiques pour le modèle de Darcy-Forchheimer en convection naturelle publication-title: Ann Fac Sci Toulouse Math doi: 10.5802/afst.666 contributor: fullname: Fabrie – volume: 59 start-page: 2911 year: 1987 ident: 10.1016/j.cnsns.2011.06.039_b0020 article-title: Exact Lyapunov dimension of the universal attractor for the complex Ginzburg–Landau equation publication-title: Phys Rev Lett doi: 10.1103/PhysRevLett.59.2911 contributor: fullname: Doering |
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| SubjectTerms | Computational fluid dynamics Convection Convection modes Descriptions Dynamical systems Low-dimensional dynamical reduction Mathematical analysis Mathematical models Number of degrees of freedom Porous medium Stability Upper bounds |
| Title | New upper bounds and reduced dynamical modeling for Rayleigh–Bénard convection in a fluid saturated porous layer |
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