A Numerical Model for Magnetohydrodynamic Waves in a Stably-Stratified Layer in Earth's Core

A numerical model for magnetohydrodynamic waves in a thin shell is developed and applied to study the effect of a stably-stratified layer in Earth's core on geomagnetic secular variation. The model employs a spherical coordinate system with finite differences in r and θ and Fourier decomposition in Φ. The model is linearized assuming a background azimuthal velocity field UΦ(r,θ) and an arbitrary background magnetic field Br,θ,Φ(r,θ). The Boussinesq approximation is employed and the buoyancy forces are prescribed in terms of a spatially variable Brunt-Vaisala frequency N(r,θ). The equations are cast into a sparse generalized eigenvalue problem by assuming solutions of the form uj,bj,p=CjeimΦ+λt and eigenmodes are found. Good agreement is obtained with previous approximate analytical solutions for zonal (m=0) magnetic-Archimedes-Coriolis (MAC) waves (e.g. Braginsky, 1993), global magnetic-Rossby (m>0) waves (e.g. Braginsky, 1998), and equatorially-trapped magnetic-Rossby waves (e.g. Bergman, 1993). This model is employed to study the origins of the fast equatorial waves observed by Chulliat et al. (2015) in recent high-resolution magnetic field models to constrain plausible properties of the stably-stratified layer and core-surface magnetic field.