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Multiple flow solutions in buoyancy induced convection in a porous square box
Author(s) -
Henry D.,
Touihri R.,
Bouhlila R.,
Ben Hadid H.
Publication year - 2012
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2012wr011995
Subject(s) - buoyancy , bifurcation , mechanics , convection , square (algebra) , flow (mathematics) , rayleigh number , bifurcation diagram , hopf bifurcation , mathematics , natural convection , thermodynamics , physics , geometry , nonlinear system , quantum mechanics
The convection induced by buoyancy effects in a porous square cavity has been investigated numerically using a spectral element code with bifurcation tools. The complex bifurcation diagram initiated from the first six primary bifurcation points corresponding to the onset of convection from the trivial no‐flow solution has been calculated. Four branches of stable steady solutions have been found, corresponding to one‐roll, two‐roll, three‐roll and four‐roll flow structures. The domain of existence of these stable solutions, i.e., the Rayleigh number (Ra) range in which such solutions can potentially be observed, has been precisely determined. It is shown that there exist Ra ranges where different flow solutions can be stable together. The stable branches all terminate at Hopf bifurcation points beyond which oscillatory solutions have been computed.