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Transitional behaviour of convective patterns in free convection in porous media

Published online by Cambridge University Press:  06 April 2017

Hamid Karani Open the ORCID record for Hamid Karani [Opens in a new window]  and
Christian Huber
Hamid Karani*
Affiliation:
School of Earth and Atmospheric Sciences, Georgia Institute of Technology, Atlanta, GA 30332-03403, USA
Christian Huber
Affiliation:
Department of Earth, Environmental and Planetary Sciences, Brown University, Providence, RI 02912, USA
*
†Email address for correspondence: hamid.karani@gatech.edu
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Abstract

The present study focuses on the transition between steady convective patterns in fluid-saturated porous media. We conduct experiments to identify the transition point from the single- to double-cell pattern in a two-dimensional porous medium. We then perform a basin stability analysis to assess the relative stability of different convective modes. The resulting basin stability diagram not only provides the domains of coexistence of different modes, but it also shows that the likelihood of finding convective patterns depends strongly on the Rayleigh number. The experimentally observed transition point from single- to double-cell mode agrees well with the stochastically preferred mode inferred from the basin stability diagram.

JFM classification

Nonlinear Dynamical Systems: Bifurcation Convection: Convection in porous media
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 818 , 10 May 2017 , R3
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Copyright
© 2017 Cambridge University Press 

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References

Beck, J. L. 1972 Convection in a box of porous material saturated with fluid. Phys. Fluids 15 (8), 1377–1383.Google Scholar
Cross, M. C. & Hohenberg, P. C. 1993 Pattern formation outside of equilibrium. Rev. Mod. Phys. 65, 851–1112.Google Scholar
Feudel, U. 2008 Complex dynamics in multistable systems. Intl J. Bifurcation Chaos 18 (6), 1607–1626.Google Scholar
Henry, D., Touihri, R., Bouhlila, R. & Ben Hadid, H. 2012 Multiple flow solutions in buoyancy induced convection in a porous square box. Water Resour. Res. 48 (10), w10538.Google Scholar
Horne, R. N. 1979 Three-dimensional natural convection in a confined porous medium heated from below. J. Fluid Mech. 92, 751–766.Google Scholar
Horton, C. W. & Rogers, F. T. 1945 Convection currents in a porous medium. J. Appl. Phys. 16, 367–370.Google Scholar
Karani, H. & Huber, C. 2015 Lattice Boltzmann formulation for conjugate heat transfer in heterogeneous media. Phys. Rev. E 91, 023304.Google Scholar
Karani, H. & Huber, C. 2017 Role of thermal disequilibrium on natural convection in porous media: insights from pore-scale study. Phys. Rev. E 95, 033123.Google Scholar
Lapwood, E. R. 1948 Convection of a fluid in a porous medium. Math. Proc. Camb. Phil. Soc. 44, 508–521.Google Scholar
Menck, P. J., Heitzig, J., Marwan, N. & Kurths, J. 2013 How basin stability complements the linear-stability paradigm. Nat. Phys. 9, 89–92.Google Scholar
Nield, D. A. & Bejan, A. 2013 Convection in Porous Media. Springer.Google Scholar
Riley, D. S. & Winters, K. H. 1989 Modal exchange mechanisms in Lapwood convection. J. Fluid Mech. 204, 325–358.Google Scholar
Schubert, G. & Straus, J. M. 1979 Three-dimensional and multicellular steady and unsteady convection in fluid-saturated porous media at high Rayleigh numbers. J. Fluid Mech. 94, 25–38.CrossRefGoogle Scholar
Sezai, I. 2005 Flow patterns in a fluid-saturated porous cube heated from below. J. Fluid Mech. 523, 393–410.CrossRefGoogle Scholar
Steen, P. H. 1983 Pattern selection for finite-amplitude convection states in boxes of porous media. J. Fluid Mech. 136, 219–241.Google Scholar
Straus, J. M. & Schubert, G. 1979 Three-dimensional convection in a cubic box of fluid-saturated porous material. J. Fluid Mech. 91, 155–165.Google Scholar
Venturi, D., Wan, X. & Karniadakis, G. E. 2010 Stochastic bifurcation analysis of Rayleigh–Bénard convection. J. Fluid Mech. 650, 391–413.Google Scholar
Zhou, J. X., Aliyu, M. D. S., Aurell, E. & Huang, S. 2012 Quasi-potential landscape in complex multi-stable systems. J. R. Soc. Interface 9, 3539–3553.Google Scholar