Single-mode theory of diffusive layers in thermohaline convection

Abstract

A two-layer configuration of thermohaline convection is studied, with the principal aim of explaining the observed independence of the buoyancy-flux ratio on the stability parameter when the latter is large. Temperature is destabilizing and salinity is stabilizing, so diffusive interfaces separate the convecting layers. The convection is treated in the single-mode approximation, with a prescribed horizontal planform and wavenumber. Surveys of numerical solutions are presented for a selection of Rayleigh numbers R, stability parameters λ and horizontal wavenumbers a. The solutions yield a buoyancy flux ratio ζ that is insensitive to ζ, in accord with laboratory experiments. However ζ increases with increasing R, in contradiction to laboratory observations.