Williams, G. P., 1970: Axisymmetric annulus convection at unit Prandtl number. Geophysical Fluid Dynamics, 1, 357-369.

Abstract: We examine the role played in annulus flows by mechanisms dependent upon the Prandtl number, sigma. Solutions are obtained at sigma = 1 for both the real annulus system and for the hypothetical "free annulus" system (free slip lateral boundaries). These solutions are compared with previously obtained solutions at sigma = 7.7.
In the free annulus, the solution at sigma = 1 differs radically from that at sigma = 7. The sigma = 1 solution appears to be essentially a finite amplitude mode due to Solberg instability whereas the solution at sigma = 7 manifests a flow caused by the diffusive overturning mechanism.
The variation with sigma of the real annulus flow is not so fundamental but some differences in the dynamical structures are noted.