Rotating magnetoconvection with anisotropic diffusivities in the Earth's core

Tomas Soltis

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. \par 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 ({\it SA}) the dominant effect on the dynamics is due to density stratification determined by gravity, ${\bm g}=−g{\bf \hat z}$, 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 ({\it BM}) anisotropy $[1]$ the dominant effect of rotation and magnetic field is supposed. The diffusive coefficients in the $z$-direction, coinciding with the vector of rotation, $\bm{\mathit{\Omega}}=\mathit{\Omega_0}{\bf \hat z}$, and in the $y$-direction of the magnetic field vector, ${\bm B}=B_m {\bf\hat y}$, are greater than in the $x$-direction. \par 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, {\it SA} and {\it BM}, are compared and their role either to facilitate or to inhibit rotating magnetoconvection is determined.

Mots clés: Anisotropic diffusive coefficients; Rotating magnetoconvection; Turbulence; Earth's core; Geomagnetic field

Tomas Soltis. Rotating magnetoconvection with anisotropic diffusivities in the Earth's core. Physics of the Earth and Planetary Interiors, 2009, 178 (1-2), pp.27. ⟨10.1016/j.pepi.2009.08.013⟩. ⟨hal-00601521⟩