The onset of convection in an anisotropic porous layer inclined at a small angle from the horizontal

Abstract

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 at a small angle to the horizontal. The aim of this work is to determine analytically by how much the critical Rayleigh number varies when the layer first ceases to be horizontal. For nearly isotropic layers we show that rolls may be either longitudinal or transverse depending on the nondimensional parameters; this is unlike the case of O(1) inclinations the results of which are presented in a companion paper.