Pattern Formation in the Rotating Cylindrical Annulus with an Azimuthal Magnetic Field at low Prandtl Numbers

Abstract

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, Ω 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 Ψ depends on the ratio between the Chandrasekhar number, Q ~ B2, and the Coriolis number, τ ~ Ω. In addition to fully three-dimensional (3 D) numerical simulations, weakly nonlinear and Galerkin analyses for roll patterns are performed for Prandtl number P = 0 .1. At finite amplitudes, secondary instabilities are encountered in the form of longwave and shortwave.