LINEAR STABILITY AT THE ONSET OF ROTATING CONVECTION IN THE PRESENCE OF MAGNETIC FIELD

Abstract

The phenomena of convection are one of the most interesting problems in fluid dynamics. In this paper we shall study the case of linear stability of a rotating electrically conducting viscous layer heated from below lying in a uniform magnetic field based on the Boussinesq approximation. We restrict our study to the case when the direction of magnetic field and rotation are parallel; the discussion is focused on the case of large Taylor number  and Chandrasekhar number . Generally, magnetic field facilitates convection in a rapidly rotating frame breaking the rotational constraints. The numerical solutions for stationary convection showed that at fixed large  and as we increase , The critical Rayleigh number  stayed fixed until  reached a special value, then as we increase , Rayleigh number continue to decrease reaching its minimum before starting to increase again, two minimum values are determined at large . A further analysis done on the stationary convection is finding the critical value of  which give the same critical Rayleigh number at large Taylor number .