A CHARACTERIZATION THEOREM IN ROTATORY HYDRODYNAMIC TRIPLY DIFFUSIVE CONVECTION WITH VISCOSITY VARIATIONS

The paper mathematically establishes that rotatory hydrodynamic triply diffusive convection with variable viscosity and one of the components as heat with diffusivity., cannot manifest itself 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)), mu(min) (the minimum value of viscosity mu in the closed interval [0,1]) and the Prandtl number s satisfy the inequality R-1+ R-2 <= 27 pi(4)/4{mu(min) +(tau 1+tau 2)/sigma/1+tau 1/tau 2} provided D-2 mu is positive everywhere and (tau 1+tau 2)/sigma <= mu(min). It is further proved that this result is uniformly valid for the quite general nature of the bounding surfaces.