Three-dimensional linear stability of natural convection in horizontal concentric annuli

We have performed three-dimensional linear stability analyses of natural convection of air (Pr = 0.71) in horizontal annuli between concentric cylinders by using a spectral element method. A linear stability theory is applied to a basic two-dimensional steady solution which is called a crescent-shaped convection, and an eigenvalue problem of matrix form is constituted. We evaluate a critical Rayleigh number where the basic flow loses its stability with respect to three-dimensional disturbances over a wide range of aspect ratio (1 ⩽ A ⩽ 20). It is found that the instability mode which destabilizes the basic convection exchanges among three different modes, and the new transition lines are proposed.