Journal of Fluid Mechanics

Solutions and stability criteria of natural convective flow in an inclined porous layer

J. P.  Caltagirone a1 and S.  Bories a2
a1 Laboratoire d'Energétique et Phénomènes de Transfert, Unité Associée CNRS n° 873, Ecole Nationale d'Arts et Métiers, Esplanade des Arts et Métiers, 33405 TALENCE CEDEX (France)
a2 Institut de Mécanique des Fluides de Toulouse, Laboratoire associé CNRS n° 5, E.N.S.E.E.I.H.T., 2 rue Charles Camichel, 31071 TOULOUSE CEDEX (France)

Article author query
caltagirone jp   [Google Scholar] 
bories s   [Google Scholar] 


Previous experiments on natural convection in a differentially heated porous layer with large lateral dimensions gave evidence for different configurations of flow. Depending on the values of the Rayleigh number, the inclination and the longitudinal extension of the layer, the three main structures observed correspond to a two-dimensional unicellular flow, polyhedral convective cells and longitudinal coils. In this paper there is a definition of the conditions necessary for these types of flow to exist using a linear stability theory and it is shown that the experimentally observed structures can be theoretically predicted by a three-dimensional numerical model based upon Galerkin's spectral method. Finally, the results of this model are used to show the influence of initial conditions on the setting up of the stationary flow.

(Published Online April 20 2006)
(Received March 27 1984)
(Revised December 4 1984)