Internal gravity waves in a stratified layer atop a convecting liquid core in a non-rotating spherical shell

Seismic and magnetic observations have suggested the presence of a stably stratified layer atop Earth's core. Such a layer could affect the morphology of the geomagnetic field and the evolution of the core, but the precise impact of this layer depends largely on its internal dynamics. Among other physical phenomena, stratified layers host internal gravity waves (IGW), which can be excited by adjacent convective motions. Internal waves are known to play an important role on the large-scale dynamics of the Earth's climate and on the long-term evolution of stars. Yet, they have received relatively little attention in the Earth's outer core so far and deserve detailed investigations in this context. Here, we make a first step in that direction by running numerical simulations of IGW in a non-rotating spherical shell in which a stratified layer lies on top of a convective region. We use a nonlinear equation of state to produce self-consistently such a two-layer system. Both propagating waves and global modes coexist in the stratified layer. We characterize the spectral properties of these waves and find that energy is distributed across a wide range of frequencies and length scales, that depends on the Prandtl number. For the control parameters considered and in the absence of rotational and magnetic effects, the mean kinetic energy in the layer is about 0.1 per cent that of the convective region. IGW produce perturbations in the gravity field that may fall within the sensitivity limit of present-day instruments and could potentially be detected in available data. We finally provide a road map for future, more geophysically realistic, studies towards a more thorough understanding of the dynamics and impact of internal waves in a stratified layer atop Earth's core.