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The predominant force balance in rapidly rotating planetary cores is betweenCoriolis, pressure, buoyancy and Lorentz forces. This magnetostrophic balanceleads to a Taylor state where the spatially averaged azimuthal Lorentz force iscompelled to vanish on cylinders aligned with the rotation axis. Any deviationfrom this state leads to a torsional oscillation, signatures of which have beenobserved in the Earth's secular variation and are thought to influence lengthof day variations via angular momentum conservation. In order to investigatethe dynamics of torsional oscillations, we perform several three-dimensionaldynamo simulations in a spherical shell. We find torsional oscillations,identified by their propagation at the correct Alfv\'{e}n speed, in many of oursimulations. We find that the frequency, location and direction of propagationof the waves are influenced by the choice of parameters. Torsional waves areobserved within the tangent cylinder and also have the ability to pass throughit. Several of our simulations display waves with core travel times of 4 to 6years. We calculate the driving terms for these waves and find that both theReynolds force and ageostrophic convection acting through the Lorentz force areimportant in driving torsional oscillations.

The dynamics and excitation of torsional waves in geodynamo simulations