Suppression of instability in rotatory hydromagnetic convection

Recently discovered hydrodynamic instability [1], in a simple Bénard configuration in the parameter regime under the action of a nonadverse temperature gradient, is shown to be suppressed by the simultaneous action of a uniform rotation and a uniform magnetic field both acting parallel to gravity for oscillatory perturbations whenever (Qσ ₁/π² + J/π⁴) > 1 and the effective Rayleigh numberR(1 -T ₀α₂) is dominated by either 27π⁴(1 + l/σ₁/4 or 27π⁴/2 according as σ₁ ≥1 or σ₁ ≤ 1 respectively. HereT ₀is the temperature of the lower boundary while α₂ is the coefficient of specific heat at constant volume due to temperature variation and σ₁,R,Q andJ respectively denote the magnetic Prandtl number, the Rayleigh number, the Chandrasekhar number and the Taylor number.