Geometry effects on Rayleigh-Bénard convection in rotating annular layers

Rayleigh-Bénard convection is investigated in rotating annular cavities at a moderate dimensionless rotation rate Ω=60. The onset of convection is in the form of azimuthal traveling waves that set in at the sidewalls and at values of the Rayleigh number significantly below the value of the onset of convection in an infinitely extended layer. The present study addresses the effects of curvature and confinement on the onset of sidewall convection by using three-dimensional spectral solutions of the Oberbeck-Boussinesq equations. Such solutions demonstrate that the curvature of the outer boundary promotes the onset of the wall mode, while the opposite curvature of the inner boundary tends to delay the onset of the wall mode. An inner sidewall with a radius as low as one tenth of its height is sufficient, however, to support the onset of a sidewall mode. When radial confinement is increased the two independent traveling waves interact and eventually merge to form a nearly steady pattern of convection.