A MATHEMATICAL THEOREM FOR THERMOHALINE CONVECTION OF THE VERONIS TYPE WITH VISCOSITY VARIATIONS

The paper mathematically establishes that thermohaline convection of t he Veronis(1) type, with the viscosity variation effects included, can not manifest itself as oscillatory motions of growing amplitude in an initially bottom heavy configuration if the thermohaline Rayleigh numb er R(S), the Lewis number tau, the Prandtl number sigma and mu(min) (m inimum value of viscosity mu in the interval [0, 1]) satisfy the inequ ality R(S) less than or equal to 27/4 pi(4)(mu(min) + tau/sigma) provi ded D-2 mu is positive everywhere. Further we prove that uniformly val id for quite general nature of the bounding surfaces. A this result si milar characterization theorem is mathematically established in the co ntext of thermohaline convection of Stern(2) type (with the viscosity variation effects included).