Mantle-induced temperature anomalies do not reach the inner core boundary

Temperature anomalies in Earth's liquid core reflect the vigour of convection and the nature and extent of thermal core-mantle coupling. Numerical simulations suggest that longitudinal temperature anomalies forced by lateral heat flow variations at the core-mantle boundary (CMB) can greatly exceed the anomalies that arise in homogeneous convection (i.e. with no boundary forcing) and may even penetrate all the way to the inner core boundary. However, it is not clear whether these simulations access the relevant regime for convection in Earth's core, which is characterized by rapid rotation (low Ekman number E) and strong driving (high Rayleigh number Ra). We access this regime using numerical simulations of nonmagnetic rotating convection with imposed heat flow variations at the outer boundary (OB) and investigate the amplitude and spatial pattern of thermal anomalies, focusing on the inner and outer boundaries. The 108 simulations cover the parameter range 10(-4) <= E <= 10(-6) and Ra = 1-800 times the critical value. At each Ra and E we consider two heat flow patterns-one derived from seismic tomography and the hemispheric Y-1(1) spherical harmonic pattern-with amplitudes measured by the parameter q(star) = 2.3, 5 as well as the case of homogeneous convection. At the OB the forcing produces strong longitudinal temperature variations that peak in the equatorial region. Scaling relations suggest that the longitudinal variations are weakly dependent on E and Ra and are much stronger than in homogeneous convection, reaching O(1) Kat core conditions if q(star) approximate to 35. At the inner boundary, latitudinal and longitudinal temperature variations depend weakly on Ra and q(star) and decrease strongly with E, becoming practically indistinguishable between homogeneous and heterogeneous cases at E = 10(-6). Interpreted at core conditions our results suggest that heat flow variations on the CMB are unlikely to explain the large-scale variations observed by seismology at the top of the inner core.