The evolution of diffusive thermohaline staircases

Abstract

Diffusive thermohaline staircases have been observed over wide regions of the Northwestern Weddell Sea in the March 1986 AMERIEZ experiments.1 The spatial distribution and temporal evolution of these staircases suggests that these layers may migrate upwards and also may bifurcate into multiple layers. These observations provided the motivation for a laboratory study of the evolution of thermohaline staircases. In the present study, a thermohaline staircase was generated by heating a stable salinity gradient from below. The thicknesses of the convecting layers, heat and salt transports across the interfaces, and migration of the interfaces due to interfacial turbulent mixing were measured. During the experiments, the interfaces and convecting layers evolve with time, ultimately assuming steady positions and thicknesses h. The experimental measurements of h, away from the bottom boundary, were found to be in good agreement with a theoretical prediction based on the assumption that a balance between the kinetic and potential energies of the turbulent eddies within the convecting layers sets the thicknesses of the convecting layers. Further, the laboratory data showed an excellent agreement with the oceanic data gathered by the previous investigators. Because of buoyancy transport across the interfaces, the stratification in the system weakens and the buoyancy jump Δb across the interfaces reduces. When the interfacial Richardson number Ri=Δbδ/w*2, where δ is the thickness of the interface and w* is the convection velocity in the layers, drops below a critical value Ric, which is about 1.5, the interfaces showed rapid migration to new quasiequilibrium levels, at which they remain stationary until Ri drops below Ric again. Flow visualization studies show that these rapid migrations are caused by engulfment of the interfacial layer fluid by the eddies of the lower, strongly convecting, layers. The experiments also show that, under certain conditions involving low heat fluxes and high density stratifications, heating of a stable salinity gradient does not lead to the formation of a thermohaline staircase structure; a criterion is developed to predict the conditions favorable for their formation. In addition, when the stratification is small and heat flux is high, the convectively mixed layer propagates upward as in a nonstratified fluid and the stratification tends to be destroyed without forming layers. The laboratory results successfully explain some of the field observations, while providing insight into the physics of thermohaline convection.