Stability analysis of dual adiabatic flows in a horizontal porous layer

A study of buoyant flow in a horizontal porous layer with adiabatic and impermeable boundaries is performed. The Darcy–Boussinesq model is used and the effect of viscous dissipation is taken into account. First, it is shown that there exist two stationary and parallel solutions (dual solutions) for each pair of prescribed values of the Gebhart number Ge and of the Péclet number Pe. These dual solutions exist as long as Ge <=3^(1/2), and they become coincident when Ge =3^(1/2). Then, a linear stability analysis of the dual solutions is performed referring both to transverse and to longitudinal rolls. This analysis reveals that one of the branches in the dual solutions space is more stable than the other. Moreover, instabilities to longitudinal rolls generally occur for values of the product GePe smaller than those needed for transverse rolls.