The influence of molecular diffusivity on turbulent entrainment across a density interface

Abstract

The rate of mixing across a density interface between two layers of liquid has been measured in a laboratory experiment which allows a direct comparison between heat and salinity transports over the same range of density differences. Low Reynolds number turbulence was produced by stirring mechanically at a fixed distance from the interface, either in one or in both layers, and the results for these two sets of experiments are also compared. The measurements cover a factor of two in stirring rate and twenty in density. Over this range of conditions the ratio of entrainment velocity to stirring velocity can be expressed as functions of an overall Richardson number Ri, and in this form the results of the one and two stirred layer experiments are indistinguishable from one another. For density differences produced by heat alone, the functional dependence is close to Ri⁻¹ except at small values of Ri where it approaches a finite limit. For experiments with a salinity difference across the interface, the mixing rate is the same as in the heat experiments at low values of Ri, but falls progressively below this as Ri is increased, with the approximate form $Ri^{\frac{3}{2}} $.

An interpretation of these results has been attempted, using a dimensional analysis and qualitative mechanistic arguments about the nature of the motion. The Ri⁻¹ dependence implies a rate of change of potential energy proportional to the rate of working by the stirrer. The decreased mixing rates for salt have been attributed to a slower rate of incorporation of an entrained element into its surroundings by diffusion, which increases the tendency for it to return to the interface and dissipate energy in wave-like motions.