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We report on axisymmetric numerical simulations of rapidly rotating spherical shells in which the axial rotation rate of the outer shell is modulated in time. This allows us to model planetary bodies undergoing forced longitudinal libration. In this study we systematically vary the Ekman number, 10−7≤E≲10−4, which characterizes the ratio of viscous to Coriolis forces in the fluid, and the libration amplitude, Δϕ. For libration amplitudes above a certain threshold, Taylor–Gortler vortices form near the outer librating boundary, in agreement with the previous laboratory experiments of Noir et al. [Phys. Earth Planet. Inter. 173, 141 (2009)]. At the lowest Ekman numbers investigated, we find that the instabilities remain spatially localized at onset in the equatorial region. In addition, nonzero time-averaged azimuthal (zonal) velocities are observed for all parameters studied. The zonal flow is characterized by predominantly retrograde flow in the interior, with a stronger prograde jet in the outer equatori...

Axisymmetric simulations of libration-driven fluid dynamics in a spherical shell geometry