Conditions for Earth-like geodynamo models

For many published dynamo models an Earth-like magnetic field has been claimed. However, it has also been noted that as the Ekman number (viscosity) is lowered to less unrealistic values, the magnetic field tends to become less Earth-like. Here we define quantitative criteria for the degree of semblance of a model field with the geomagnetic field, based on the field morphology at the core–mantle boundary. We consider the ratio of the power in the axial dipole component to that in the rest if the field, the ratios between equatorially symmetric and antisymmetric and between zonal and non-zonal non-dipole components, and a measure for the degree of spatial concentration of magnetic flux at the core surface. We also briefly discuss shortcomings of possible other criteria for an Earth-like model. We test the compliance with our criteria for a large number of dynamo models driven by imposed temperatures at their inner and outer boundaries that cover the accessible parameter space. We order models according to their magnetic Reynolds number Rm (ratio of advection to diffusion of magnetic field) and magnetic Ekman number Eη (ratio between rotation period and magnetic diffusion time). Requirements for an Earth-like field morphology are that Eη < 10− 4 and that Rm falls into a limited range that depends on Eη. Higher values of Rm are required at low values of Eη. Extrapolating the boundaries of compliant dynamos in this parameter space to the Earth's value of Eη suggests that Earth-like dynamos exist all the way between present model values and parameter values of the geodynamo. We also study a more limited set of dynamo models with flux boundary conditions. The nature of the boundary condition and the distribution of sources and sinks of buoyancy have a secondary influence on the field morphology.