Boundary Condition for the Electric Field in Earth's Core Models With Conducting Boundaries

Abstract The Earth's core flows are governed by magnetohydrodynamic equations, where boundary conditions determine how the electric field in the liquid core relates to that in the conducting boundaries. In the Earth's core, the no‐slip condition implies continuity of the electric field, following the continuous horizontal velocity field. However, numerical models often employ a free‐slip condition, permitting discontinuities in horizontal velocity at the boundary, raising concerns about assuming electric field continuity, as first principles indicate the electromotive force should be continuous. Using a simple numerical model, we assess these assumptions under the free‐slip condition and compare it with the no‐slip case. Our results show that electric field continuity is appropriate when core and boundary conductivities are equal, accurately capturing shear flow near the boundary. However, with a conductivity contrast, neither electric boundary condition performs well, suggesting the free‐slip condition should be avoided in such cases.