Abstract
Two-dimensional thermal convection in a rapidly rotating cylindrical annulus is examined by the characteristics of topographic Rossby waves in order to understand the spiraling columnar convection appearing in rotating spherical systems. The top and the bottom boundaries of the annulus are inclined with respect to the rotation axis to model a spherical geometry. Through the topographic β effect of these boundaries, the rotation of the system affects two-dimensional columnar fluid motion.
The spiraling structure of critical convection obtained by linear stability analysis can be interpreted as the outward propagation of Rossby waves from the inner region, where convective motion is easily excited because of the small inclination of the boundaries. The flow pattern estimated with the dispersion relation well coincides with the structure of convection. The kinetic energy budget analysis shows that energy generated by buoyancy force in the inner region is transported by Rossby waves and dissipates in the whole region.
Mean flow generation by finite amplitude spiraling convection can be explained qualitatively by the properties of Rossby waves. Through the outward propagation of Rossby waves, whose momentum is in the prograde direction, prograde and retrograde mean flow is generated at the outer and the inner regions, respectively.
