Rotating magnetoconvection with anisotropic diffusivities in the Earth’s core

Abstract

The influence of anisotropic diffusive coefficients on stability of the horizontal fluid planar layer rotating about vertical axis and permeated by a horizontal homogeneous magnetic field is studied. The linear stability analysis is performed using separable solutions in the form of horizontal rolls. Both, stationary and overstable motions, are examined. Two basic cases of anisotropic diffusive processes are considered in the Cartesian coordinate system with the vertical in the z-direction. In the case of stratification anisotropy ( SA) the dominant effect on the dynamics is due to density stratification determined by gravity, g = − g z ˆ , which is the source of Archimedean buoyancy force. Thus, the diffusive coefficients have different values in the z-direction from those in the horizontal directions, x and y. In the case of Braginsky–Meytlis ( BM) anisotropy ( Braginsky and Meytlis, 1990) the dominant effect of rotation and magnetic field is supposed. The diffusive coefficients in the z-direction, coinciding with the vector of rotation, Ω = Ω 0 z ˆ , and in the y-direction of the magnetic field vector, B = B m y ˆ , are greater than in the x-direction. The effect of anisotropy is most evident for values of the Elsasser number similar to those estimated for the Earth’s core conditions. Both types of diffusive coefficient anisotropies, SA and BM, are compared and their role either to facilitate or to inhibit rotating magnetoconvection is determined. It was found, that investigated anisotropies influence not only the system stability conditions but also properties of arising instabilities. Two types of anisotropy, SA anisotropy of atmospheric type and BM, facilitate the onset of convection, but SA of oceanic type inhibits it. Our anisotropic studies’ results are compared and discussed with isotropic studies by Eltayeb (1972, 1975), Jones and Roberts (2000) and Roberts and Jones (2000).