Two-and three-dimensional linear convection in a rotating annulus

An exceptional case to the model-independent theory of Knobloch (1995) is presented, by investigating a rotating cylindrical annulus of height H and side wall radii r o and r i , with non-slip, perfectly thermally conducting side walls and thermally insulating stress-free ends. Radial heating permits the possibility of either two- or three-dimensional convective solutions being the preferred mode. An analytical solution is obtained for the two-dimensional case and a numerical solution for the three-dimensional solution, which is also applied to the two-dimensional solution. It is shown that both two- and three-dimensional solutions can be realized depending on the aspect ratio, γ = H/d, where d = r o -r i is the thickness of the annulus, the radii ratio λ = r i /r o and the rotation rate of the model. For γ = O(1) and λ = 0.4, the preferred convective solution is three-dimensional when the Taylor number, T < 10 2 and two-dimensional for T > 10 2 . For small aspect ratios, γ ≪ 1, the preferred mode is two-dimensional for all rotation rates.