Geomagnetic semblance and dipolar-multipolar transition in top-heavy double-diffusive geodynamo models

Convection in the liquid outer core of the Earth is expected to be driven by thermal and chemical density perturbations. The difference between the two buoyancy sources has been ignored in the majority of geodynamo models published to date. The main purpose of this study is to examine the impact of double-diffusive convection on magnetic field generation by means of three-dimensional global geodynamo models. We focus here on the "top-heavy" regime, when both thermal and compositional background gradients are destabilizing. We compute 79 numerical dynamo models spanning various fractionning of buoyancy sources. Using a linear eigensolver, we show that the onset of convection is facilitated by the addition of a second buoyancy source. The critical onset mode is similar to classical thermal Rossby waves observed with the codensity formalism. Using a rating parameter to quantify the morphological semblance of the models magnetic field with the geomagnetic field, we show that a good agreement can be attained for any partitioning of the convective input power. Next, we show that the transition between dipolar and multipolar dynamos strongly depends on the nature of the buoyancy forcing. A scale-dependent analysis of the force balance at work instead reveals that the dipole breakdown occurs when the ratio of inertia to Lorentz force at the dominant convective flow lengthscale reaches 0.5, independently of the distribution of input power between thermal and compositional buoyancies. The ratio of integrated kinetic to magnetic energy $E_k/E_m$ appears to be a reasonable proxy of this force ratio. Given that $E_k/E_m\approx 10^{-4}-10^{-3}$ in the Earth's core, the geodynamo should operate far from this transition. It hence appears unlikely that the occurrence of geomagnetic reversals is related to dramatic and punctual changes of the amplitude of inertial forces in the Earth's core.