Publications &
Communications

The length of the day variations on periods of five to hundred years are mainly due to a torque at the core-mantle boundary (CMB). We investigate how the CMB topography affects the pressure coupling in the presence of rotation, buoyancy, and magnetic effects. In our case, the pressure coupling originates from an imposed differential velocity. Using a local model of the CMB, we adopt a semi-analytical spectral method based on the physical eigenmodes of the problem. This model enables us to calculate weakly non-linear flows at the CMB and to characterise the wave drag mechanism. We incorporate planetary curvature effects by considering a "non-traditional $\beta$-plane" approximation. This enable us to extend the investigate range of topography wavelength. Our analysis reveals the significant impact of the Rossby waves on the boundary stress. We also show that these waves are drastically modified when considering three-dimensional topographies instead of simple ridges. The non-linear interaction of the waves build an average flow that is found to reduce the differential velocity.

Physicists face major challenges in modelling multi-scale phenomena that are observed in geophysical flows (e.g. in the Earth's oceans and atmosphere, or liquid planetary cores). In particular, complexities arise because geophysical fluids are rotating and subject to density variations, but also because the fluid boundaries have complex geometries (e.g. the ocean floor) with wavelengths ranging from metres to thousands of kilometres. Models of planets' fluid layers and their consequences on the dynamics of the whole celestial object are constrained by observations, whose interpretation necessitates a comprehensive understanding of the underlying physics. Geophysical studies often entail combining cutting-edge experiments across a wide range of parameters, together with theory and limited numerical simulations, to derive predictive scaling laws applicable for planetary settings. In this review, we discuss experimental efforts that have contributed to our understanding of geophysical flows with topography. More specifically, we focus on (i) the flow response to mechanical (orbital) forcings in the presence of a large-scale (ellipsoidal) topography, (ii) some effects of small-scale topography onto bulk flows and boundary-layer dynamics, and (iii) the interaction between convection and roughness. For each case, the geophysical context is briefly introduced and some experimental perspectives are drawn.

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.