Magnetic reversal frequency scaling in dynamos with thermochemical convection

• We develop scaling laws for polarity reversal frequency from numerical dynamos.
• We demonstrate that reversal frequency correlates with core heat flow.
• Our results suggest that geomagnetic superchrons occur when core heat flow is low.
• Our results also suggest that frequent reversals occur when core heat flow is high.

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 RoℓRoℓ of the convection. With uniform core–mantle boundary (CMB) heat flux, polarity reversals are absent below a critical value Roℓcrit≃0.05Roℓcrit≃0.05, beyond which reversal frequency increases approximately linearly with RoℓRoℓ. The relative standard deviation of the dipole intensity fluctuations increases with reversal frequency and RoℓRoℓ. With heterogeneous CMB heat flux that models the large-scale seismic heterogeneity in Earth’s lower mantle, reversal frequency also exhibits linear dependence on RoℓRoℓ, 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 Roℓ⩽RoℓcritRoℓ⩽Roℓcrit during magnetic superchrons and higher, more heterogeneous CMB heat flux with Roℓ>RoℓcritRoℓ>Roℓcrit 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 RoℓcritRoℓcrit enhanced equatorial cooling at the CMB increases reversal frequency by concentrating magnetic flux at low latitudes, whereas far beyond RoℓcritRoℓcrit enhanced polar cooling at the CMB increases reversal frequency by amplifying outer core convection.