Penetration of Alfvén waves into an upper stably-stratified layer excited by magnetoconvection in rotating spherical shells

The penetration of magneto-hydrodynamic (MHD) disturbances into an upper strongly stratified stable layer excited by magnetoconvection in rotating spherical shells is investigated. An analytic expression for the penetration distance is derived by considering perturbations of a stably stratified rotating MHD Boussinesq fluid in a semi-infinite region, with the rotation axis and a uniform magnetic field tilted relative to the gravity axis. Solutions for the response to MHD disturbances applied at the bottom boundary show that the disturbances propagate as Alfvén waves in the stable layer. Their propagation distance is proportional to the Alfvén wave speed and inversely proportion to both the arithmetic average of viscosity and magnetic diffusion and the total wavenumber of the disturbance. The derived expression for penetration distance is in good agreement with the numerical results for neutral convection in a rotating spherical shell with an upper stably stratified layer embedded in an axially uniform basic magnetic field.