Torsional Oscillations in a Numerical Geodynamo Operating in a Regime of Low Ekman and Magnetic Prandtl Numbers

Numerical simulations of geodynamo are carried out to understand the dynamic state of the Earth's core. Our model core consists of an electrically conducting, rotating Boussinesq fluid spherical shell and a solid inner core which has the same conductivity as the outer core and is free to rotate about the rotation axis by magnetic and viscous torques. Thermal convection occurs by simultaneous effects of secular cooling and heating at the inner core boundary. The Ekman number is 5 × 10-7, the magnetic Ekman number is 2.5 × 10-6, and the magnetic Prandtl number is 0.2, by which we aim to analyze a dynamic state in which the kinetic/magnetic energy ratio and the contribution of the viscous force are both small. A main target of this study is to elucidate torsional oscillations in the core. Theoretical study predicts that the torsional oscillations have a decadal time-scale in the Earth's core and might be responsible for observed variations of length of day through exchange of angular momentum between the core and the mantle. We expect that viscous damping of waves can be reduced by lowering the magnetic Prandtl number and advection plays a secondary role in the wave equation because of low magnetic Ekman number. As the Rayleigh number is increased from 640 to 6400, the kinetic and the magnetic energies increase almost linearly with the Rayleigh number, by their ratio being about 0.1 throughout. At the highest Rayleigh number, the volume-averaged Elsasser number in the core reaches 0.7. The zonal velocity averaged on a cylindrical surface coaxial with the rotation axis is analyzed as a function of radius of the cylinder s and time t. Outside the tangent cylinder (s>0.35), a clear wave-like signature is found in st-space. There are both ingoing and outgoing waves whose phase velocity agrees with theoretical estimates. The Lorentz force acting on the cylindrical surface dominates the viscous force, as anticipated. However, the advection term is still of the same order as the Lorentz force in the wave equation, indicating a magnetostrophic balance is incomplete. The dynamical regime may be compared with that of Dumberry and Bloxham (Phys. Earth Planet. Inter. 140, 29, 2003). We will discuss the results of wave analysis and will present results of numerical calculations at lower Ekman numbers.