Spectral Properties of Magnetohydrodynamic Convection With a Horizontal Temperature Gradient

Spectral properties of convective magnetohydrodynamic (MHD) turbulence in two and three dimensions are studied by means of direct numerical simulations. The system is set up with a mean horizontal temperature gradient in order to avoid the development of elevator instabilities in a full periodic box. All simulations are performed without mean magnetic field. The applied resolution is 5123 and 20482. The MHD equations are solved using a standard pseudospectral scheme. For removing of aliasing errors a spherical truncation method is employed. Systems are compared with predictions of various existing phenomenological theories for magnetohydrodynamic and convective turbulence. While the three dimensional system most probably operates in a Kolmogorov-like regime where buoyant forces have negligible impact on the turbulence dynamics (relatively low Rayleigh number achieved in the simulation; Ra~106), the two dimensional system exhibits interesting irregular oscillations between a buoyancy dominated Bolgiano-Obukhov-like regime and a Iroshnikov-Kraichnan-like turbulence. The most important parameter determining the regime of 2D magnetoconvection apart from the Rayleigh number seems to be the mutual alignment of velocity and magnetic fields. The non-linear dynamics and the interplay between individual fields are examined with different transfer functions that confirm basic assumptions about directions of energy transfer. Kinetic, magnetic and temperature energy are transported in the turbulent cascade from large to smaller scales.