Magnetic reversal frequency scaling in dynamos with thermochemical convection

Scaling relationships are derived for the frequency of magnetic polarity reversals in numerical dynamos powered by thermochemical convection. We show that the average number of reversals per unit of time scales with the local Rossby number Ro ℓ of the convection. With uniform core–mantle boundary (CMB) heat flux, polarity reversals are absent below a critical value Ro ℓ crit ≃ 0.05 , beyond which reversal frequency increases approximately linearly with Ro ℓ . The relative standard deviation of the dipole intensity fluctuations increases with reversal frequency and Ro ℓ . With heterogeneous CMB heat flux that models the large-scale seismic heterogeneity in Earth’s lower mantle, reversal frequency also exhibits linear dependence on Ro ℓ , and increases approximately as the square root of the amplitude of the CMB heterogeneity. Applied to the history of the geodynamo, these results imply lower CMB heat flux with Ro ℓ ⩽ Ro ℓ crit during magnetic superchrons and higher, more heterogeneous CMB heat flux with Ro ℓ > Ro ℓ crit when geomagnetic reversals were frequent. They also suggest that polarity reversals may have been commonplace in the early history of other terrestrial planets. We find that zonal heterogeneity in CMB heat flux produces special effects. Close to Ro ℓ crit enhanced equatorial cooling at the CMB increases reversal frequency by concentrating magnetic flux at low latitudes, whereas far beyond Ro ℓ crit enhanced polar cooling at the CMB increases reversal frequency by amplifying outer core convection.