Formation of thermoclines in zero-mean-shear turbulence subjected to a stabilizing buoyancy flux

Abstract

Laboratory experiments in which a stabilizing buoyancy flux is imposed on zero-mean-shear turbulence generated by an oscillating grid are discussed. The buoyancy flux is imposed at the top of a water column either as a constant heat flux or by the continuous addition of fresh water at the top of a salt solution. Two types of experiments were carried out. In the first, the oscillating grid was positioned near the buoyancy input plane at the top of the water column to represent an input of turbulence kinetic energy near the surface. In this case a mixed layer was formed which extended from the surface down to a finite depth, and was bounded below by a stable thermocline. The mixed-layer depth remained constant in time but, contrary to earlier suggestions, was not found to be proportional to the Monin-Obukhov length. Instead the depth of the mixed layer was found to depend on the rate of decay of the turbulent kinetic energy with depth through the mixed layer. A second set of experiments was carried out with the grid positioned well below the surface to represent turbulence produced by bottom stirring. At low values of the buoyancy flux the fluid column remained well mixed, but once the buoyancy flux exceeded a critical value a stable stratification built up near the surface. Under certain conditions, a steady stratification was produced in which the diffusive flux balanced the turbulent flux in the mixed layer below. At larger values of the buoyancy flux, the diffusive flux is not large enough to remove the buoyancy from the surface and a ‘runaway’ stratification develops. The criterion for the formation of surface stratification is also found to depend on the rate of decay of the turbulent kinetic energy with depth, and the implications of this work for the formation of fronts produced by tidal stirring are discussed.