Upper limits to the complex growth rates in thermohaline instability

AbstractThe paper presents a significant improvement on Banerjee et al.'s results [Proc. Roy. Soc. London Ser. A 378 (1981), 301–304] which prescribe upper limits to the complex growth rates of arbitrary oscillatory motions of growing amplitude in thermohaline instability. The modified results derived here are of wider generality and applicability than the simple context in which they are presented and lead in the context of Veronis' configuration to an alternative nondimensional system of governing equations and boundary conditions of thermohaline instability in terms of a new nondimensional number B, on which the nonexistence of oscillatory motions of growing amplitude crucially depends