New upper bounds and reduced dynamical modeling for Rayleigh-Bénard convection in a fluid saturated porous layer

Communications in Nonlinear Science and Numerical Simulation

Volumn 17, Issue 5, 2012, Pages 2191-2199

  Wen, Baole ^a   Dianati, Navid ^b   Lunasin, Evelyn ^b   Chini, Gregory P ^a,c   Doering, Charles R ^b  

^a UNIVERSITY OF NEW HAMPSHIRE   (United States)

^b UNIVERSITY OF MICHIGAN   (United States)

^c University of New Hampshire   (United States)

Author keywords

Convection; Low dimensional dynamical reduction; Number of degrees of freedom; Porous medium; Stability

Indexed keywords

DEGREES OF FREEDOM (MECHANICS); DYNAMICAL SYSTEMS; TRANSPORT PROPERTIES;

% REDUCTIONS; CONVECTION; DYNAMICAL MODELING; FLUID-SATURATED POROUS LAYERS; LOW DIMENSIONAL; LOW-DIMENSIONAL DYNAMICAL REDUCTION; NUMBER OF DEGREES OF FREEDOM; POROUS MEDIUM; RAYLEIGH; UPPER BOUND;

POROUS MATERIALS;

EID: 82955248162     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2011.06.039     Document Type: Article

References (19)

1. Busse F., Joseph D. Bounds for heat transport in a porous layer. J Fluid Mech 1972, 54:521-543.
2. Chini G.P., Dianati N., Zhang Z., Doering C.R. Low dimensional models from upper bound theory. Physica D 2011, 240:241-248.
3. Doering C.R., Constantin P. Bounds for heat transport in a porous layer. J Fluid Mech 1998, 376:263-296.
4. Doering C.R., Gibbon J.D., Holm D.D., Nicolaenko B. Exact Lyapunov dimension of the universal attractor for the complex Ginzburg-Landau equation. Phys Rev Lett 1987, 59:2911-2914.
5. Efendiev M.A., Fuhrmann J., Zelik S.V. The long-time behaviour of the thermoconvective flow in a porous medium. Math Methods Appl Sci 2004, 27:907-930.
6. Fabrie P. Solutions fortes et comportement asymptotique pour un modle de convection naturelle en milieu poreux. Acta Appl Math 1986, 7:49-77.
7. Fabrie P. Solutions fortes et majorations asymptotiques pour le modèle de Darcy-Forchheimer en convection naturelle. Ann Fac Sci Toulouse Math 1989, (5 1):7-26.
8. Fabrie P. Attracteurs pour deux modèles de convection naturelle en milieux poreux. CR Acad Sci Paris Sér I Math 1990, 311:407-410.
9. Graham M.D., Steen P.H. Plume formation and resonant bifurcations in porous-media convection. J Fluid Mech 1991, 272:67-89.
10. Gupta V., Joseph D. Bounds for heat transport in a porous layer. J Fluid Mech 1973, 57:491-514.
11. Hamilton J.M., Kim J., Waleffe F. Regeneration mechanisms of near-wall turbulence structures. J Fluid Mech 1995, 287:317-348.
12. Holmes P.J., Lumley J.L., Berkooz G. Turbulence, Coherent Structures, Dynamical Systems and Symmetry 1996, Cambridge University Press, Cambridge and New York.
13. Howard L.N. Heat transport by turbulent convection. J Fluid Mech 1963, 17:405-432.
14. Jiménez J., Moin P. The minimal flow unit in near-wall turbulence. J Fluid Mech 1991, 225:213-240.
15. Joseph D.D. Stability of Fluid Motions. I, II 1976, Springer-Verlag, Berlin and New York.
16. Otero J., Dontcheva L.A., Johnston H., Worthing R.A., Kurganov A., Petrova G., et al. High-Rayleigh-number convection in a fluid-saturated porous layer. J Fluid Mech 2004, 500:263-281.
17. Robinson J.C. Infinite-Dimensional Dynamical Systems 2001, Cambridge University Press, Cambridge.
18. Temam R. Infinite-Dimensional Dynamical Systems In Mechanics and Physics 1997, Springer-Verlag, New York.
19. Vitanov N.K. Upper bounds on the heat transport in a porous layer. Physica D 2000, 136:322-339.