Gravitationally driven inner core differential rotation

A heterogeneous heat flux at the core-mantle boundary can maintain time-averaged convective structures in the fluid core. This includes a steady pattern of heterogeneous heat flux at the inner core boundary which leads to aspherical inner core growth. If this growth pattern is longitudinally misaligned with the mantle-induced geoid, the latter would impart a gravitational torque on the newly created topography of the inner core. Allowing for continuous melting/solidification and viscous deformation of the inner core, a steady gravitationally driven differential rotation of the inner core with respect to the mantle can be sustained. In this work, we present calculations of inner core rotation driven by such a mechanism using recently published models of the heat flux at the inner core boundary and of the geoid at the base of the mantle. We show that, for a fast mean inner core growth rate of 1 mm/yr and a bulk viscous relaxation time longer than 100 yr, the inner core differential rotation can be as high as 100 deg/Myr, in the westward direction. Although this is much too slow (and in the wrong direction) to explain the seismically inferred inner core rotation (eastward, of the order of 0.2 deg/yr), this mechanism by itself would rotate the inner core by one full rotation in only a few million years. This gravitational torque would then partly offset the viscomagnetic torque from the steady eastward zonal flow near the inner core boundary, the driving mechanism typically invoked to explain a steady inner core super-rotation. Under the combined action of these two torques, the overall steady differential rotation of the inner core may then be small. This would allow the development of an inner core texture with a distinct longitudinal pattern connected to its aspherical freezing rate, as has been suggested to explain seismic observations.