Pattern Formation of Rotating Magnetoconvection with Anisotropic Thermal Diffusivity Effect in the Earth's Outer Core

The rotation rate and the magnetic field play a key role, in the geodynamo models, for understanding the convective flow behavior in the Earth’s outer core where dynamic MAC balance of forces occurs frequently and is affected by the diffusion processes. Due to the presence of buoyancy, Lorentz and Coriolis forces, the turbulent eddies in the core get deformed and elongated in the direction parallel to the rotation axis and magnetic field in BM anisotropy or are affected by gravity (buoyancy) direction in SA anisotropy. Hence the turbulence is highly anisotropic. The turbulent small-scale eddies are diffusers of momentum and heat, and thus, the effective viscosity and thermal diffusion are also anisotropic. The effect of anisotropic thermal diffusion coefficient on the stability of horizontal fluid planer layer heated from below and cooled from above, rotating about its vertical axis and subjected to a uniform horizontal magnetic field, is analyzed in the present study. The cross, oblique and parallel rolls assumed to make an angle (θ), 90°, 0° < θ < 90° and 0°, respectively, with the axis of the magnetic field. These rolls are calculated for different range of control parameters arising in the system. The linear stability analysis is investigated by using the normal mode method. The appearance of rolls for stationary modes as well as oscillatory modes depends on the SA (Stratification Anisotropy) parameter, α (the ratio of horizontal and vertical thermal diffusivities). The stabilizing/destabilizing effect strongly depends on the Chandrasekar (Q) and Taylor (Ta) numbers. The obtained results for isotropic cases coincide with those obtained by pioneers in the literature. The two-dimensional anisotropic complex Ginzburg-Landau (ACGL) equation with cubic nonlinearity is used to study the weakly nonlinear behaviour near the primary instability threshold. This equation, derived using the multiple scale analysis, is similar to the one found in the literature. The numerical simulation of this ACGL equation with periodic boundary conditions has been carried out using the pseudo-spectral method in Fourier space with exponential time differencing. The formation of spatiotemporal patterns strongly depends on α, Ta and Q. For fixed Q, as Ta increases, the Coriolis force intensifies, more stable and organized spiral patterns showed their presence. Further for increasing Ta, the size or scale of spiral patterns decreases, while the number of patterns get increased.