Characterization of rotatory hydrodynamic triply diffusive convection

The present paper mathematically establishes that rotatory hydrodynamic triply diffusive convection with one of the components as heat with diffusivity \({\kappa }\) cannot manifest as oscillatory motions of growing amplitude in an initially bottom heavy configuration if the two concentration Rayleigh numbers R 1 and R 2, the Lewis numbers \({\tau _1}\) and \({\tau _2}\) for the two concentrations with diffusivities \({\kappa _1}\) and \({\kappa _2}\), respectively (with no loss of generality \({\kappa > \kappa _{1} > \kappa _2 )}\) and the Prandtl number \({\sigma }\) satisfy the inequality \({R_1 +R_2 \leq \frac{27\pi ^{4}}{4} \left( {\frac{1+\frac{\tau _1 +\tau _2 }{\sigma }}{1+\frac{\tau _1 }{\tau _2 ^{2}}}} \right)}\). It is further established that this result is uniformly valid for the quite general nature of the bounding surfaces.