www.elsevier.com/locate/cam Boundary layer instability at the top of the Earth’s outer core

We investigate the instability of mixed Ekman–Hartmann boundary layers arising in rotating incompressible magnetohydrodynamics 6ows in a parameter regime relevant to the Earth liquid core. Relying on the small depth of the boundary layer, we perform a local study in a half-space at a given co-latitude = =2, and assume a mean dipolar axial magnetic:eld with internal sources (the geodynamo). Instabilities are driven, for high enough Reynolds number, by the quadratic term in the momentum equation. Nonlinear stability can be proven using energy methods in the neighborhood of the poles (Nonlinearity 1