Publications &
Communications

While mechanical couplings between fluid and solid domains have been widely studied, their estimation remains challenging for deep planetary fluid layers with buoyancy, magnetic field, and topographic effects. Results from atmospheric or oceanic sciences are unsuitable for thick layers such as subsurface oceans of icy moons, or liquid cores of planets. Rapid rotation and/or the presence of a magnetic field in these regions may also cause difficulties. Considering a rotating and stratified fluid layer, we have developed an asymptotic local model to investigate the small-scale topographic fluid-solid coupling due to pressure or magnetic stresses. Our code unlocks several previous limitations of planetary coupling studies. Considering three-dimensional bumps, it provides the fluid stress on an electrically conducting solid (e.g. the mantle lowermost layer). We explore a wide range of parameters and boundary conditions for arbitrary topography shapes, and account for planetary curvature effects by considering a "non-traditional β-plane" approximation. Carrying out a detailed study of the wave drag mechanism, we show that the Rossby planetary waves, which are absent from recent asymptotic models, can significantly modify the boundary stress. We also show that the results are drastically different when considering 3D topographies instead of ridges.

In planetary fluid cores, the density depends on temperature and chemical composition, which diffuse at very different rates. This leads to various instabilities, bearing the name of double-diffusive convection (DDC). We investigate rotating DDC (RDDC) in fluid spheres. We use the Boussinesq approximation with homogeneous internal thermal and compositional source terms. We focus on the finger regime, in which the thermal gradient is stabilizing whereas the compositional one is destabilizing. First, we perform a global linear stability analysis in spheres. The critical Rayleigh numbers drastically drop for stably stratified fluids, yielding large-scale convective motions where local analyses predict stability. We evidence the inviscid nature of this large-scale double-diffusive instability, enabling the determination of the marginal stability curve at realistic planetary regimes. In particular, we show that in stably stratified spheres, the Rayleigh numbers Ra at the onset evolve like Ra ∼ Ek⁻¹, where Ek is the Ekman number. This differs from rotating convection in unstably stratified spheres, for which Ra ∼ Ek^−4/3. The domain of existence of inviscid convection thus increases as Ek^−1/3. Secondly, we perform non-linear simulations. We find a transition between two regimes of RDDC, controlled by the strength of the stratification. Furthermore, far from the RDDC onset, we find a dominating equatorially antisymmetric, large-scale zonal flow slightly above the associated linear onset. Unexpectedly, a purely linear mechanism can explain this phenomenon, even far from the instability onset, yielding a symmetry breaking of the non-linear flow at saturation. For even stronger stable stratification, the flow becomes mainly equatorially symmetric and intense zonal jets develop. Finally, we apply our results to the early Earth core. Double diffusion can reduce the critical Rayleigh number by four decades for realistic core conditions. We suggest that the early Earth core was prone to turbulent RDDC, with large-scale zonal flows.