Impact of boundary condition on the onset of thermo-chemical convection at the Earth’s core

The geomagnetic fields are generated by dynamo action driven by thermo-chemical convection in the deep interior. The convective instability occurs due to the density gradient of fluid, which depends on the temperature (thermal) and light element concentration (chemical composition), and they diffuse at different rates. We investigate rotating double-diffusive convection (RDDC) in the two-dimensional plane layer. We focus on classical convection, a diffusive regime with unstable thermal and chemical composition gradients. A systematic investigation on the impact of various thermal and compositional boundary conditions, such as fixed temperature, fixed composition, fixed heat flux, and fixed compositional flux, and their combinations, on the onset of convection by fixing mechanical boundary condition as no-slip is carried out in the present study. In particular, we choose a compositionally dominated regime by fixing the Rayleigh ratio (ratio of thermal to compositional Rayleigh number) equal to 0.5 for both non-rotating and rotating cases. With varying compositional Rayleigh numbers, the critical thermo-chemical Rayleigh number is estimated at the onset. The onset Rayleigh number, with fixed temperature and compositional boundary condition at both the upper and bottom boundary, is higher than fixed flux conditions for both the non-rotating and rotating cases, and this trend persists with increase (decrease) in compositional (thermal) Prandtl number at the low diffusivity ratio regime. However, at the high diffusivity ratio regime, the trends substantially change with changing diffusivity.