The onset of convection in an inclined anisotropic porous layer

We consider the onset of convection in a porous layer heated from below. The layer is anisotropic with respect to both its permeability and diffusivity and is inclined to the horizontal. The aim of this work is to determine not only by how much the critical Rayleigh number varies when the layer is inclined, but also the wave number and the angle the roll makes with the direction about which the layer is inclined. We find that there is not always an abrupt transition between longitudinal and transverse rolls as the governing parameters are varied, but there is often a smooth transition between these states.