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 behavior at low viscosity. This regime is computationally very demanding, which has prompted us to adopt a plane layer model with an inclined rotation vector, and to make use of efficiently parallelized code. No hyperdiffusion is used, all diffusive operators are in the classical form. Our model has infinite Prandtl number, a Rayleigh number that scales as $E^{-1/3}$ $(E$ being the Ekman number), and a constant Roberts number. The optimized model allows us to study dynamos with Ekman numbers in the range $\left[{10}^{-5}{,10\mathrm{}}^{-4}\right].$ 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) a MAC balance within the bulk, i.e., Coriolis, pressure, Lorentz, and buoyancy forces are of comparable magnitude, while viscous forces are only significant in thin boundary layers, (ii) the Elsasser number is $O\left(10\right),$ (iii) the strong magnetic fields cannot prevent small-scale structures from becoming dominant over the large-scale components, (iv) the Taylor-Proudman effect is detectable, (v) the Taylorization decreases as the Ekman number is lowered, and (vi) the ageostrophic velocity component makes up $80\%$ of the flow.

• Received 10 October 2001

DOI:https://doi.org/10.1103/PhysRevE.66.056308