Pattern formation of mixed convection in a porous medium confined laterally and heated from below: effect of inertia

We consider the onset of convection in a porous medium heated from below and subjected to a horizontal mean flow. The effect of porous inertia is studied, and the transverse aspect ratio a of the medium is taken into accout. We find that the dominant modes are longitudinal rolls (L.R) if a is an integer or transverse traveling rolls (T.R) if a is below a(c) with a(c) < 1. When a is not an integer with a > a(c), the setting on patterns are oscillatory three-dimensional structures (3D) for a > 1 or T.R for a(C) < a < 1 provided that the Reynolds number remains below a critical value Re-K*. We show that these structures are replaced by K L.R if Re-K > Re-K* (C) 2002 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.