On Thermohaline Convection of the Veronis Type

In the present paper we prove that thermohaline convection of the type described by G. Veronis (J. Mar. Res.23, 1965, 1) cannot manifest as oscillatory motions of growing amplitude in an initially bottom heavy configuration if the thermohaline Rayleigh number Rs, the Lewis number τ, and the Prandtl number σ satisfy the inequality Rs ≤ (27π4/4)(l + τ/σ). Further we prove that this result is uniformly valid for the quite general nature of the bounding surfaces.