Horizontal mixing in lakes

Horizontal mixing in the upper hypolimnion of lakes far from the boundaries was studied in lake basins with surface areas between 5 and 220 km2 by observing the growth of the concentration distribution of the fluorescent dye sodium fluorescein(uranin). In each of the eight experiments, between 0.2 and 2 kg of uranin was instantaneously released into the lake in the appropriate depth (between 15 and 25 m) in such a way to keep the initial cloud size as small as possible. The horizontal extension of the cloud was repeatedly determined by integration of numerous vertical profiles. These surveys served to test theoretical models for horizontal mixing. The temporal development of the size and of the variances along the principal axes of the tracer concentration distribution was the main property considered here. The experiments cover a range of cloud sizes between 3 X 102 and 3 X 105 m2. None of them support the hypothesis that cloud size grows with elapsed time raised to the power of 3 as predicted by the inertial subrange turbulence model first applied to dispersion by Batchelor [1950]. The shear-diffusion model of Carter and Okubo [1965] was found to provide a good description of the development of cloud size with time. This model also accounts for the fact that the tracer distributions were not radially symmetric. Effective horizontal diffusivities lie between 0.02 and 0.3 m2 S-l. Reevaluation of published data from experiments in Lake Ontario [e.g., Murthy, 1976] and in the ocean [e.g., Okubo, 1971] supports both the applicability of the shear-diffusion model and the doubts raised against the appropriateness of the inertial subrange model for scales up to 1000 m.