Numerical study on double-diffusive convection in the Earth’s core

Our numerical study focuses on convection in a rotating spherical shell with the objective to model combined thermal and compositional convection as proposed for the Earth’s core. Since the core is cooling, a thermal gradient is established, which can drive thermal convection. Simultaneously, due to the solidification of the inner core latent heat is released at the freezing front and the concentration of the light constituents of the liquid phase increases thus providing a source for compositional buoyancy. Typically, the molecular diffusivities of both driving components differ by some orders of magnitude. To account for this difference it is indicated to adopt a double-diffusive convection model in treating Earth’s core dynamics. As opposed to purely thermal or purely compositional convection the double-diffusive system is controlled by two Rayleigh numbers associated with the respective buoyancy sources. Using the Rayleigh numbers as control parameters neutral curves of the linear onset of convection in the rotating shell are determined for different Ekman numbers and diffusivity ratios. It is found that the neutral curves depend significantly on the system parameters. By comparison with the analytical solutions of the rotating cylindrical annulus it is shown that the neutral curves represent a superposition of curves associated with solutions for different azimuthal wave numbers. Furthermore, fully non-linear simulations are presented in order to elucidate the effect of isochemical and fixed chemical flux boundary conditions on the convection. We consider three driving scenarios with varying thermo-chemical forcing ratios. Both the forcing ratio and the chemical boundary condition have distinct effects on the system that are discussed separately.