Kinetic energy budget analysis of spiraling columnar critical convection in a rapidly rotating spherical shell

Abstract

The kinetic energy budget analysis of spiraling columnar critical convection emerging in a rapidly rotating spherical shell is performed. In the cylindrical-radially elongated spiraling convection mode appearing as a critical mode at small Prandtl numbers, the kinetic energy generated in the inner region of the spherical shell is transported in a cylindrically radial manner and is dissipated near the outer boundary around the equator. However, when the Prandtl number is increased, the dynamical energy flux turns in the axial direction rather than in the cylindrically radial direction. The kinetic energy generated inside the shell is transported in the direction of the rotating axis and is dissipated near the outer boundary at the same cylindrically radial location. The existence of the axial component of the dynamical energy flux is attributed to the ageostrophic flows in the columnar vortices induced by viscous damping and buoyancy force. In spite of the existence of the axial component of dynamical energy flux, the obtained geometry of the axially integrated kinetic energy budget is consistent with the results using a two-dimensional rotating annulus model. Therefore, the interpretation of spiraling structure with the radial propagation properties of topographic Rossby waves is applicable to the three-dimensional spiraling columnar convection emerging in a rotating spherical shell. Flow patterns calculated from the dispersion relation of two-dimensional topographic Rossby waves in a rotating spherical shell well explain the structure of the three-dimensional spiraling columnar convection.