Evolution of Kelvin-Helmholtz billows in nature and laboratory

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A mixing mechanism prevalent in natural flows is the formation and breakdown of vortical billows known as Kelvin-Helmholtz (K-H) instabilities. Here we present field examples of K-H billow occurrences in the atmosphere and oceans. Laboratory experiments aimed at studying certain key features of K-H billows are also discussed, wherein the billows were generated in a two-layer stratified tilt-tank. It is shown that small-scale turbulent mixing is present within billows from the early stages of their evolution, but mixing becomes intense and the billows are destroyed as they achieve a maximum height and initiate collapse at a non-dimensional time of ΔUt/λ ≈ 5, where ΔU is the velocity shear and λ is the wavelength. When γ Ut/λ < 5, the Thorpe scale LT and the maximum Thorpe displacement (LT)max, normalized by the local billow height Lb, are independent of both the horizontal location within the billow and time with LT/Lb ≈ (0.49 ± 0.03) and (LT)max/Lb ≈ (0.89 ± 0.02). After the collapse starts, however, the pertinent lengthscale ratios in the 'core' of the billow show values similar to those of fully developed turbulent patches, i.e., LT/Lb ≈ (0.29 ± 0.04) and (LT)max/Lb ≈ (0.68 ± 0.04). The field observations were found to be in good agreement with laboratory-based predictions.

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Earth and Planetary Science Letters