Onset of convection in an anisotropic porous medium with oblique principal axes

Abstract

We investigate the onset of Rayleigh–Bénard convection in a horizontal porous layer with anisotropic permeability. The permeability is transversely isotropic, whereas the orientation of the longitudinal principal axes is arbitrary. This is sufficient to achieve qualitatively new flow patterns with a tilted plane of motion or tilted lateral cell walls. The critical Rayleigh number and wavenumber at marginal stability are calculated. There are two different types of convection cells (rolls): (i) the plane of motion is tilted, whereas the lateral cell walls are vertical; (ii) the plane of motion is vertical, whereas the lateral cell walls are tilted as well as curved. It turns out that type (i) occurs when the transverse permeability is larger than the longitudinal permeability, and for the converse case type (ii) is preferred.