Three-dimensional convection driven by centrifugal buoyancy

Convection driven by centrifugal buoyancy in a cylindrical fluid annulus cooled from the inside, heated from the outside, and rotating about its axis is described. While at high values of the dimensionless rotation parameter τ convection rolls aligned with the axis are preferred, three-dimensional patterns of convection are introduced at low values of τ through either the cross-roll instability or a subharmonic varicose instability. The instabilities are studied in terms of simple analytical relationships as well as through numerical methods based on the Galerkin scheme. Analytical expressions for the steady three-dimensional patterns induced by the instabilities are also derived.