Pattern formation in the rotating cylindrical annulus with an azimuthal magnetic field at low prandtl numbers

Patterns are theoretically formed in the frame of a hydromagnetic convection induced by radial buoyancy in an electrically conducting fluid contained by a rotating cylindrical annulus with a homogeneous magnetic field (B) in the azimuthal direction. The annulus is assumed to rotate with an angular frequency, 92 under the small gap approximation with rigid cylindrical boundaries. The onset of convection is found in the form of axial, axisymmetric or oblique rolls with a broken symmetry. The roll angle T depends on the ratio between the Chandrasekhar number, Q similar to B-2, and the Coriolis number, tau similar to Omega. In addition to fully three-dimensional (3D) numerical simulations, weakly nonlinear and Galerkin analyses for roll patterns are per-formed for Prandtl number P = 0.1. At finite amplitudes, secondary instabilities are encountered in the form of longwave and shortwave.