Numerical investigations of rotating MHD in a spherical shell

Motions of liquid metal inside the Earth’s outer core are responsible for generating the geomagnetic field in a dynamo process. We use a pseudo-spectral magnetohydrodynamic code to investigate dynamos maintained by various mechanisms. Boundary conditions (BC) and governing parameters are varied with the purpose of modelling the Earth’s core. An accurate means to benchmark codes with so-called pseudo-vacuum magnetic BCs is proposed and an alternative way to drive a laboratory dynamo, by fluid injection is investigated. Many prominent features in the observed core surface magnetic field are not yet explained due to the intrinsic complexity of the system and the difficulty in solving the model equations with the Earth’s core parameters. It is however possible to gradually advance the models towards a geophysically relevant parameter regime as greater computing resources become available. We present dynamo simulations at rapid rotation rates (E = ν/(2Ωd) = 3 · 10−7 and 10−6) that are at the cutting edge of geodynamo research today. We vary the convection strength by a factor of 30 and ratio of magnetic to viscous diffusivities by a factor of 20 (0.05 ≤ Prm ≤ 1) using a heat flux outer BC. This regime has been little explored due to significant computing resources required: several tens of millions cpu-hours were consumed to obtain the presented results. We report energy spectra of steady solutions, a comparison of volumeintegrated characteristics of fields with the proposed rotating convection and dynamo scaling laws, timeand longitudeaverages of force and energy balances, and the structure of the dynamos deep in the shell and on the CMB in relation to the selection of control parameters. Insulating magnetic boundary conditions (used for the mentioned above big runs) are not easy to implement in non-spectral codes. A more convenient pseudo-vacuum boundary condition (setting to zero tangential magnetic field) may be used instead for practical reasons. We present essential properties of two dynamo solutions with regular deterministic characteristics operating with pseudo-vacuum BCs. One of them has been used in the community benchmark paper (Jackson et al., 2014). We also present analytical solutions for the decay rates of magnetic field decay modes in a sphere and in a spherical shell. We investigate in addition the capability of a laboratory dynamo to be driven by the fluid injection (from one boundary and draining off from another boundary). A linear calculation is used to delineate the curve defining the onset of non-axisymmetric velocity modes: these modes are only possible in a limited range of injection strengths and rotation rates. We also conduct a set of experiments with the magnetic induction equation included and identified dynamos in several cases.