  Palaeomagnetic evidence shows that the behaviour of the geodynamo has changed
during geological times. Variations in the heat flux at the core-mantle
boundary (CMB) due to mantle convection could be responsible. Previous studies,
based on unrealistically viscous dynamo simulations, have shown that
large-scale CMB heat flux heterogeneities impact the magnetic dipole stability.
To better understand how they affect the geodynamo, we used several
simulations, ranging from standard numerical dynamos to more extreme
parameters, including strong-field cases and turbulent cases. We show that
heterogeneities with realistic amplitudes can favour a multipolar dynamo by
either forcing equatorially antisymmetric zonal flows or eastward zonal flows.
Strong-field dynamo models are found to be less sensitive, due to significant
westward flows. We also find that the dipolar fraction of the magnetic field is
best captured by $M^*=M\ E_{\eta}\ \dfrac{l_c}{\pi}$ where $M$ is the magnetic
to kinetic energy ratio, $E_{\eta}$ is the magnetic Ekman number, and $l_c$ is
the dominant harmonic degree of the flow, with multipolar dynamos found at
lower $M^*$. $M^*$ estimated for the Earth's core is consistent with a
reversing dipolar magnetic field. Within the range of $M^*$ susceptible to
reversals, breaking the equatorial symmetry or forcing eastward zonal flows in
our simulations consistently triggers reversals or a transition towards
multipolar dynamos. Our results support that time variations of heat-flux
heterogeneities driven by mantle convection through Earth's history are capable
of inducing the significant variations in the reversal frequency observed in
the palaeomagnetic record.
