Dynamics of mixed convective--stably-stratified fluid, a numerical approach in spherical geometry
M. Bouffard, B. Favier and M. Le Bars
The Earth possesses a magnetic field that protects the terrestrial atmosphere from harmful Solar winds. This implies that at least part of the Earth’s liquid outer core is vigorously convecting, in order to generate the geomagnetic field through dynamo action. Yet, recent seismic and magnetic observations suggest that a stably stratified layer exists below the core mantle boundary, at the top of the convecting region (figure 1). The generation of the geomagnetic field, its morphology and evolution with time therefore depend on the dynamics of this two-layer system.
Among the various phenomena that can develop in the stable layer are internal waves, that can be excited by the convection underneath. These may affect the structure and time evolution of the magnetic field. For example, Buffett (2014) showed that a certain type of waves, called MAC waves - which can develop within the stratified layer from the interplay between Magnetic, Archimedes and Coriolis forces - can in theory explain a 60-year fluctuation in the geomagnetic dipole and provide a good description of time-dependent zonal flow at the top of the core, as inferred from geomagnetic secular variation. However, the dynamics of internal waves within a stably stratified layer at the top of the core has not yet been studied in numerical simulations. Using a slightly modified version of the PARODY code (J. Aubert, E. Dormi), we perform a first numerical exploration of the dynamics of these waves in a 3D rotating spherical shell.
Ref:
Buffett, B. (2014). Geomagnetic fluctuations reveal stable stratification at the top of the Earth’s core. Nature, 507(7493), 484-487.
Helffrich, G., & Kaneshima, S. (2010). Outer-core compositional stratification from observed core wave speed profiles. Nature, 468(7325), 807-810.
Figure 1: simplified cartoon of the structure of the Earth's core, made of a solid inner core and a fluid outer core. The latter consists of a convecting region in contact with a top stratified layer. Convective motions can excite waves at the interface with the stable layer. Conversely, the dynamics of the stratified layer can affect the convective dynamics underneath.
Emergence of a mean zonal flow in the stratified layer
We run simulations of convection at low Prandtl number, devoid of turbulence, in a 3D spherical shell, with a stratified layer in the top half of the shell. In the absence of rotation, no mean flow develops (on sufficiently long time averages), since the sphere is isotropic and there is no privileged direction. Adding slow rotation (that does not influence the convective part or very little) is enough to break the isotropy in the stable layer and produce a mean zonal flow at low latitudes (figure 2c). Increasing the rotational constraint to Rossby~1 dramatically strengthens this flow (figure 2d). Eventually, a rotationally influenced regime is reached for the convection, with a completely different dynamics that we are currently investigating. If such a mean zonal flow exists at the top of the core, it may have strong implications for the structure and time evolution of the geomagnetic field. In future simulations, we will therefore include magnetic effects.
Figure 2: azimuthal section showing the zonal velocity, time averaged over about 1.5 viscous times (0.15 thermal diffusive times). Rossby numbers are computed in the convective region (bottom half of the shell). The colorscale applies to all figures. However, for a better visualization, the velocities inside the stratified layer (top half of the shell), have been multiplied by a factor 10 for cases (a), (b) and (c).
Figure 3: axial vorticity of the radial velocity (amplified in the stratified region for a better visualization), in the equatorial plane.
Waves excitation by turbulent convection in a 3D spherical shell
We are running 3D numerical simulations of the convective--stably-stratified system in a non-rotating spherical shell. Convection is characterised by relatively high, turbulent Reynolds numbers, resulting in computationally expensive simulations. Waves are excited at the impact points of plumes (figure 3) and show a concentric propagation. We are currently quantifying the spectral distribution of the wave energy in wave number-frequency space, to better assess the effect of these waves on the global dynamics of the core.
Last updated: July 2020