Equatorially trapped waves in a stratified region in the Earth’s outer core modeled using 2-layer shallow water equations

Near the equatorial region of the Earth’s core, secular variation in the geomagnetic field consists of short period fluctuations. Such fluctuations in the magnetic field are believed to be the result of equatorially trapped waves close to the core-mantle boundary. The balance between the magnetic, Coriolis and buoyancy forces can sustain waves if a stably stratified layer exists in the outermost regions of the core. In this study, a shallow water model with additional magnetic field effects has been used to investigate the characteristics of such equatorially trapped waves. A two-layer model is studied analytically to investigate the effects of radially varying background magnetic fields on the equatorially confined MAC waves. Dispersion relations obtained are significantly influenced by the dependency of the second layer pressure gradient on that of the first layer.  Moreover, the reduced gravity effects in the second layer also modifies the second layer dynamics. Additional parameters, formulated in terms of density, magnetic field strength and buoyancy frequency of both layers characterize the system. The modified properties of a two layer model compared to a single layer is investigated for various regimes of such control parameters. It is found that the alteration in the second layer’s buoyancy frequency significantly influences the dynamics of the MAC (Magnetic-Archimedes-Gravity) wave.