On the characterization of magnetohydrodynamic triply diffusive convection

The present paper mathematically establishes that magnetohydrodynamic triply diffusive convection with one of the components as heat, with diffusivity κ, cannot manifest 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 κ1 and κ2 respectively (with no loss of generality κ0>κ1>κ2) and the Prandtl number σ satisfy the inequality R1+R2≤(27π4/4)((1+((τ1+τ2)/σ))/(1+(τ1/τ22))). It is further established that this result is uniformly valid for any combination of rigid and/or free perfectly conducting boundaries.