J. Rotvig and C.A. Jones
School of Mathematical Sciences, University of Exeter, England
We present a fully 3d self-consistent convection-driven dynamo model with reference to the geodynamo. A relatively low Ekman number regime is reached, with the aim of investigating the dynamical behaviour at low viscosity. This regime is very demanding computationally, so a plane layer model with an inclined rotation vector is adopted, and efficiently parallelised codes are used. No hyperdiffusion is used, all diffusive operators having the classical form. Our model has infinite Prandtl number, a Rayleigh number which scales as $E^{-1/3}$ ($E$ being the Ekman number), and constant Roberts number. The optimized model allows us to study dynamos with Ekman numbers in the range $[10^{-5},10^{-4}]$. In this regime we find strong-field dynamos where the induced magnetic fields satisfy Taylor's constraint to good accuracy. The solutions are characterized by (i) Lorentz, Coriolis, pressure and buoyancy forces are of the same order of magnitude, while viscous forces are only significant in thin boundary layers, (ii) The Elsasser number is $O(10)$, (iii) The Taylor-Proudman effect is detectable, (iv) The Taylorisation decreases as the Ekman number is lowered, and (v) The ageostrophic velocity component makes up $80\%$ of the flow.