Résumé
Fan-type sandstone deposits within a sedimentary basin generally present an anisotropic structure with maximum permeability in the paleo-horizontal direction. Modelling of 3-D circulations in inclined isotropic porous layers suggests the following patterns of fluid motion: for subcritical Rayleigh numbers Ra the fluid circulates along the steepest slope: this is the well known basic flow; at low inclinations, the supercritical convection consists in polyhedric cells and beyond a critical slope of 32°, longitudinal coils (i.e. with axes parallel to the steepest slope) are the preferential mode of convection. We extend these results to anisotropic media, with anisotropies up to 1000, by means of 3-D numerical modelling. From a systematic linear study near the critical Rayleigh number Rac it turns out that the critical slope lowers to 12.7°, 4.2°, 1.4° for anisotropy ratios of 10, 100, 1000 respectively. A complete non-linear study at twice the critical Rayleigh number and for a slope of 2° presents only longitudinal rolls; their width is lower than four when the anisotropy does not exceed 1000. Moreover we observe that the circulation of the fluid particles inside the coil follows a loop stretched in the slope direction with a length of six and 60 times the thickness of the layer, for anisotropies of 100 and 1000 respectively. We suggest that this offers a possibility of very far transport of minerals in the direction of the slope.