A Hybrid Finite-Volume Fourier Method for Modeling Wave Dynamics in a Stably-Stratified Core

We develop a numerical model to study magnetohydrodynamic waves in a thin buoyant layer of fluid in a rotating spherical geometry. This model combines finite-volume and Fourier methods to permit a general description of the layer geometry and other factors that control the wave dynamics, including the main magnetic field. Such a layer has been proposed on the basis of many different chemical and physical arguments and has implications for Earth's evolution and thermal state, although its existence is still debated. The combination of buoyancy, rotation, and magnetic forces permit large-scale and long-period waves that contribute to geomagnetic secular variation. Numerical results for several idealized cases are presented and compared with previous analytical and numerical solutions to verify the methodology. We also make comparison to recent geomagnetic observations of equatorially trapped waves to place constraints on conditions near the top of the core.