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Seismic studies indicate that the Earth's inner core has a complex structureand exhibits a strong elastic anisotropy with a cylindrical symmetry. Among thevarious models which have been proposed to explain this anisotropy, one classof models considers the effect of the Lorentz force associated with themagnetic field diffused within the inner core. In this paper we extend previousstudies and use analytical calculations and numerical simulations to predictthe geometry and strength of the flow induced by the poloidal component of theLorentz force in a neutrally or stably stratified growing inner core, exploringalso the effect of different types of boundary conditions at the inner coreboundary (ICB). Unlike previous studies, we show that the boundary conditionthat is most likely to produce a significant deformation and seismic anisotropyis impermeable, with negligible radial flow through the boundary. Exactanalytical solutions are found in the case of a negligible effect of buoyancyforces in the inner core (neutral stratification), while numerical simulationsare used to investigate the case of stable stratification. In this situation,the flow induced by the Lorentz force is found to be localized in a shear layerbelow the ICB, which thickness depends on the strength of the stratification,but not on the magnetic field strength. We obtain scaling laws for thethickness of this layer, as well as for the flow velocity and strain rate inthis shear layer as a function of the control parameters, which include themagnitude of the magnetic field, the strength of the density stratification,the viscosity of the inner core, and the growth rate of the inner core. We findthat the resulting strain rate is probably too small to produce significanttexturing unless the inner core viscosity is smaller than about $10^{12}$ Pa.s.

Earth's Inner Core dynamics induced by the Lorentz force