In 1990, scientists released uranin 15 metres deep in Switzerland’s Lake Alpnach to track mixing; the dye cloud stretched into an elongated streak as currents moved it

AI Representation: A fluorescent green uranin dye cloud stretches through Lake Alpnach as underwater currents carry it into an elongated plume. Image credits: ChatgptA container with the fluorescent dye was placed on Lake Alpnach, a 4.5 - 4.8 km² basin of Lake Lucerne in central Switzerland, by Swiss scientists in 1990 as part of a series of tracer experiments later reported in the Journal of Geophysical Research. They released between 0.2 and 2 kg of uranin at depths of 15–25 m below the surface. This experiment had a simple idea behind it but a difficult execution: to trace how a small concentrated blob of dye would spread in still lake water under the action of invisible currents. Over the following days, the scientists returned repeatedly to profile the evolving dye cloud and map its shape and concentration.Uranin dye at 15 meters, chosen for two reasonsSodium fluorescein, better known as uranin, was used because it does not adsorb to suspended particles and breaks down easily in sunlight and acidic conditions. It was injected at 15 meters deep because, at this depth, it lies within the hypolimnion, the layer below the thermocline where wind-driven surface mixing is minimal. Wind-driven mixing is not the only force at work in the hypolimnion, however; slower currents and shear can still act within this layer, and it was this shear that stretched the dye cloud into an elongated streak. This experiment, referred to as the 'Alp' run in the 1996 paper's data tables, is one of eight experiments the same team conducted on four lakes in Switzerland, with basins varying from 4.5 to 220 square kilometers and with 0.2 to 2 kilograms of uranin injected at depths of 15 to 25 meters in each case. This research was published in the paper titled Horizontal Mixing in Lakes in the Journal of Geophysical Research in 1996, by Frank Peeters, Alfred Wüest, Gabriel Piepke and Dieter Imboden. The dye was injected instantaneously and the cloud was tracked by integrating many vertical profiles over time. The paper reports cloud areas ranging from 3 × 10² to 3 × 10⁵ m², with effective horizontal diffusivities of 0.02 to 0.3 m² s⁻¹ and no support for the Batchelor inertial‑subrange prediction.Carter and Okubo's shear model, not Batchelor's turbulence modelRather than expanding into a neat, ever-widening circle, the patch stretched into an elongated streak as it drifted and the same asymmetry showed up across all eight trials in the study. The scientists made a comparison between the cloud growth that was observed and two different theories, Batchelor's 1950 theory of turbulence of the inertial subrange type for horizontal diffusion and the shear-diffusion theory based on the work of Carter & Okubo (1965). The data were inconsistent with Batchelor's prediction, while the shear-diffusion theory fit the observations better. These tracer cloud sizes, which increased from about 300 to 300,000 m2 throughout the experiment, did not increase with time in accordance with Batchelor’s inertial subrange theory. Rather, a shear diffusion model proved very applicable and provided the answer to why these clouds were never radially symmetric; the reason is that the currents on one side of the cloud moved at a different speed/direction compared to those on the opposite side of the cloud.In another study, this time with drifters rather than dyes in Lake Constance, Frank Peeters and Hilmar Hofmann confirmed the hypothesis. According to Frank Peeters and Hilmar Hofmann's article "Length-Scale Dependence of Horizontal Dispersion in the Surface Water of Lakes," published in Limnology and Oceanography in 2015 and listed on the University of Konstanz's publication page, constant shear in a current causes the dispersion coefficient to increase linearly with the size of the moving cloud. As reported in the study, the dispersion coefficients ranged from 0.01 to 0.03 square meters per second at a length scale of 100 meters, and from 0.1 to 0.7 square meters per second at a length scale of 1,000 meters. However, this linear relationship describes an idealized case of constant shear; when the researchers analyzed their actual field data, the model showed clear limitations.View over Stansstad of Lake Alpnach in Central Switzerland. Image credits: Wikimedia CommonsShear accounted for less than 40% of the scale dependence between 100 and 1,000 meters. It seems that the process of turbulent diffusion accounted for the scale-dependence effect greatly and that the shear influenced only the orientation of the drifting clouds. As stated in the paper, drifters were deployed in Lake Constance in four experiments, with groups of 14 to 17 drifters spanning length scales from 30 to 3,000 meters. As stated by the researchers, the dispersion coefficient had oscillatory properties and could be explained by shear diffusion and basin-scale seiching and not by a length-scale law.An effective diffusivity between 0.02 and 0.3 square meters per secondFor all eight deployments, including the Alpnach deployment, the 1996 paper mentioned above computed effective horizontal diffusivities in the range of 0.02 to 0.3 square meters per second, numbers that were many orders of magnitude higher than the diffusivity due to molecular diffusion alone. After subtracting the effect of velocity shear from the total diffusivity, the estimated turbulent diffusivity fell to 0.02 to 0.18 square meters per second.Eawag, the institute behind both studiesThe Alpnach experiment is a useful example because a measured mass of dye was placed at a known depth and left to the lake's natural processes. In addition, the results showed long before the advent of satellite tracking or drifters that even a small group of researchers could obtain useful data on mixing using only dye and a fluorometer. Eawag, the Swiss Federal Institute of Aquatic Science and Technology, employed the authors of both papers discussed here and continues to run comparable lake research today, now paired with sensors and modeling tools that reduce the need for repeated manual sampling. In essence, the 1990 experiment showed that, apparently, still lakes contain water flows strong enough to turn a concentrated kilogram of dye into a thin spreading cloud within hours and that the process can be measured and reproduced in another Swiss lake 25 years later.