Influence of surface displacement on solid state flow induced by horizontally heterogeneous Joule heating in the inner core of the Earth

• Surface displacement vanishes when turbulent velocity u′u′ is large.
• Surface displacement develops when u′u′ is small.
• Radial flow at ICB emerges when u′u′ is large.
• Radial flow at ICB vanishes when u′u′ is small.
• Values of u′u′ should be 10-1-10-210-1-10-2 m/s to explain elastic anisotropy.

We investigate the influence of surface displacement on fluid motions induced by horizontally heterogeneous Joule heating in the inner core. The difference between the governing equations and those of Takehiro (2011) is the boundary conditions at the inner core boundary (ICB). The temperature disturbance at the ICB coincides with the melting temperature, which varies depending on the surface displacement. The normal component of stress equalizes with the buoyancy induced by the surface displacement. The toroidal magnetic field and surface displacement with the horizontal structure of Y20 spherical harmonics is given. The flow fields are calculated numerically for various amplitudes of surface displacement with the expected values of the parameters of the core. Further, by considering the heat balance at the ICB, the surface displacement amplitude is related to the turbulent velocity amplitude in the outer core, near the ICB. The results show that when the turbulent velocity is on the order of 10-110-1–10-210-2 m/s, the flow and stress fields are similar to those of Takehiro (2011), where the surface displacement vanishes. As the amplitude of the turbulent velocity decreases, the amplitude of the surface displacement increases, and counter flows from the polar to equatorial regions emerge around the ICB, while flow in the inner regions is directed from the equatorial to polar regions, and the non-zero radial component of velocity at the ICB remains. When the turbulent velocity is on the order of 10-410-4–10-510-5 m/s, the radial component of velocity at the ICB vanishes, the surface counter flows become stronger than the flow in the inner region, and the amplitude of the stress field near the ICB dominates the inner region, which might be unsuitable for explaining the elastic anisotropy in the inner core.