Rotating convection in stably-stratified planetary cores
Résumé
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 $Ra \sim Ek^{-1}$, where $Ek$ is the Ekman number.
This differs from rotating convection in unstably-stratified spheres, for which $Ra \sim Ek^{-4/3}$.
Second, we perform nonlinear simulations.
We find a transition between two regimes of RDDC, controlled by the strength of the stratification.
For strong stable straficiation, 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.
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