A Characterization Theorem in Magnetohydrodynamic Triply Diffusive Convection with Viscosity Variations

The paper mathematically establishes that magnetohydrodynamic triply diffusive convection, with variable viscosity and with one of the components as heat with diffusivity κ, cannot manifest itself as oscillatory motions of growing amplitude in an initially bottom heavy configuration if the two concentration Rayleigh numbers R₁ and R₂, the Lewis numbers τ₁ and τ₂ for the two concentrations with diffusivities k₁ and k₂ respectively (with no loss of generality κ > κ₁ > κ₂), μ_min (the minimum value of viscosity μ in the closed interval [0,1]) and the Prandtl number σ satisfy the inequality R₁ + R₂ ≤ 27π⁴/4{μ_min+(τ₁+τ₂)/σ/1+τ₁/τ²₂ provided D²μ is positive everywhere. It is further proved that this result is uniformly valid for any combination of rigid and/or free perfectly conducting boundaries.