Implication of the lopsided growth for the viscosity of Earth's inner core

A particular mode of convection, called translation, has recently been put forward as an important mode of inner core dynamics because this mechanism is able to explain the observed east–west asymmetry of P-wave velocity and attenuation (Monnereau et al., 2010). Translation is a particular solution to Navier–Stokes equation with permeable boundary conditions, but depending on the viscosity of the solid core, modes with higher spherical harmonics degree can develop. At low viscosity, these modes can be dominant and dissipate the degree l=1 of thermal heterogeneities. Hence, a viscosity threshold may be expected below which translation cannot take place, thereby constraining the viscosity of iron at inner core conditions.Using a hybrid finite-difference spherical harmonics Navier–Stokes solver, we investigate here the interplay between translation and convection in a 3D spherical model with permeable boundary conditions. Our numerical simulations show the dominance of pure translation for viscosities of the inner core higher than 4×1018Pas. Translation is almost completely hampered by convective motions for viscosities lower than 1017Pas and the phase change becomes an almost impermeable boundary. Between these values, a well developed circulation at the harmonic degree l=1 persists, but composed of localized cold downwellings, a passive upward flow taking place on the opposite side (the melting side). Such a convective structure remains compatible with the seismic asymmetry.

► Seismic asymmetry of the inner core can be explained by a translational motion.
► We model the interplay of translation with convection in spherical geometry.
► Whatever the Rayleigh number, translation establishes for a viscosity greater than 4×1018Pas.
► Below 4×1018Pas, the convection hampers the translation.
► Seismic asymmetry of the inner core constraints the lower bound of the viscosity of solid iron around 1018Pas.