Two-dimensional spiraling convection in a rapidly rotating cylindrical annulus and the dynamics of Rossby waves

Shin-ichi Takehiro and Masanori Irie
(Faculty of Sciences, Kyushu Univ.)

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 b effect of these boundaries, the rotation of the system affects two-dimensional columnar fluid motion.

Linear stability analysis shows that a pattern of critical convection spreads in the radial direction spirally at small Prandtl numbers. The convective pattern shrinks towards the inner region as the Prandtl number is increased. The spiraling structure 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 top and bottom boundaries. The flow pattern estimated with the dispersion relation of Rossby waves well coincides with the structure of convection. When the Prandtl number is increased the effect of viscosity becomes large and Rossby waves cannot propagate outward. The kinetic energy budget analysis of critical convection shows that energy generated by buoyancy force in the inner region is transported by the Rossby waves and dissipates in the whole region.

Numerical calculations show that finite amplitude spiraling convection generates mean zonal flow whose direction is prograde in the outer region and retrograde in the inner region. The mean flow generation can be explained qualitatively by the properties of Rossby waves. Since the the momentum of Rossby waves is in the prograde direction and they are emitted from the inner region, the momentum is decreased there and retrograde mean flow is generated, while the momentum is increased and prograde mean flow is induced in the outer region where the waves converge and dissipate.

Spiraling convection appearing in rapidly rotating spherical systems is expected to be interpreted by the characteristics of Rossby waves in the same way as the system of the rotating annulus.