Rotating double-diffusive convection in stably stratified planetary cores

Abstract

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. We investigate rotating double-diffusive convection (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 stabilising whereas the compositional one is destabilising. 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 . Second, we perform nonlinear 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 anti-symmetric, 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 nonlinear 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.

On the Evolution of Thermally Stratified Layers at the top of Earth’s Core

“…Our model of stable layer dynamics involves a simple parameterisation of entrainment by the underlying convection and also ignores double diffusive effects that may arise from thermally stable and chemically unstable conditions at the top of the core. This configuration is well known to be unstable to 'finger' convection (Turner, 1973;Monville et al, 2019), which can lead to the emergence of large-scale structures in the form of thermo-chemical staircases (Garaud, 2018) and zonal flows (Monville et al, 2019). However, adding either or both of these effects only acts to reduce the thickness of a stable layer and so the results we have obtained in their absence should provide an upper bound on the thickness of a thermally stable layer in Earth's core.…”

The effects of a Robin boundary condition on thermal convection in a rotating spherical shell

“…We use the eigenvalue solver SINGE (freely available at ; Vidal & Schaeffer 2015; Monville et al. 2019) in order to determine the critical Rayleigh number of the system, , and, in terms of spherical harmonics, the order of azimuthal symmetry of the most unstable mode at the onset of convection in our system. SINGE is a Python code conceived to determine the eigenvalues and eigenmodes of incompressible and stratified fluids in spherical cavities.…”

Turbulent Viscosity Acting on the Equilibrium Tidal Flow in Convective Stars

“…Lai et al 1993). We employ dimensionless quantities for the simulations, adopting R as the length scale, the viscous timescale R 2 /ν as the timescale, and (νQ T R 2 )/(6κ 2 ) as the unit of temperature (as in Monville et al 2019). The dimensionless equations for u and the temperature perturbation Θ, in the inertial frame, are…”