Limitations to the Growth Rate of Perturbation in Rotatory Convection in Couple-Stress Fluid in the Presence of Magnetic Field

The thermal instability of a couple-stress fluid acted upon by uniform vertical magnetic field and rotation heated from below is investigated. Following the linearized stability theory and normal mode analysis, the paper through mathematical analysis of the governing equations of couple-stress fluid convection with a uniform vertical magnetic field and rotation, for the case of rigid boundaries shows that the complex growth rate σ of oscillatory perturbations, neutral or unstable for all wave numbers, must lie inside a semi-circle

σ²_r + σ²_i Q²[1-T_A/{2π²(1+π²F)-1}]^-2,

in the right half of a complex σ-plane, where Q is the Chandrasekhar number, T_A is the Taylor number, and F is the couple-stress parameter, which prescribes the upper limits to the complex growth rate of arbitrary oscillatory motions of growing amplitude in a rotatory couple-stress fluid in porous medium heated from below.