Rotating Magnetoconvection with Diffusivities Parameterized by Turbulent State of the Earth's Core

In rotating magnetoconvection (RMC) models, the turbulent state of the Earth's fluid core is parameterized by the isotropic (i) and anisotropic (a) diffusive coefficients, specifically, the viscosity (ν), thermal diffusivity (κ), and magnetic diffusivity (η). It can be used as the basic state, which is useful for the study of stability analysis as each physical state. The linear stability analysis is performed on RMC model of the horizontal fluid planar layer heated from below and cooled from above, rotating about its vertical axis and permeated by a horizontal homogeneous magnetic field. The normal mode method in the form of horizontal rolls is applied on the RMC model. A comparison is made between the results based on the fastest growing (F) modes with the highest growth rate and the marginal (M) modes. The F modes are studied for four different i and a combinations of diffusivities (νκη) = (aaa, aai, iai, iii) as (f, p, h, i) cases. Both the anisotropic and isotropic parameters have a significant impact on the instability caused by a large Rayleigh number, R, in all occurrences of F modes. The F modes are strongly and differently influenced by the f, p, h and i, cases. In all the investigated cases the wave number and maximum growth rate based on the R and the anisotropic parameter, α (ratio of horizontal to vertical diffusivities), are independent of Ekman number, E_z, Elsasser number, Λ_z and are the same. The effect of all anisotropy cases is more significant for the F modes than the M modes on the occurrence of convection modes. The F modes show much better results than the M modes related to the parameters, R, E_z, Λ_z, inverted magnetic Prandtl number, p_z , and Roberts number, q_z that are typical for the Earth’s outer core. The present RMC approach allows to easily deal with very huge R, very small E_z  and huge wave numbers, particularly in F modes which the geodynamo simulations are unable to do. In M as well as in F modes, the inequality α > 1 (α < 1) inhibits (facilitates) the convection, at all anisotropy cases. The QG balance of forces could prevail in α << 1 conditions in the Earth's outer core and the MAC balance could be in the uppermost layer of the core with α >> 1.

Keywords: Rotating magnetoconvection; fastest growing modes; marginal modes; anisotropic diffusivities; molecular and turbulent diffusivities; Earth’s core conditions.