Evolution of Kelvin-Helmholtz billows in nature and laboratory

Abstract

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 TUt λ < 5 , the Thorpe scale L T and the maximum Thorpe displacement ( L T) max, normalized by the local billow height L b, are independent of both the horizontal location within the billow and time with L T L b ≈ (0.49 ± 0.03) and (L T) max L b ≈ (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., L T L b ≈ (0.29 ± 0.04) and (L T) max L b ≈ (0.68 ± 0.04) . The field observations were found to be in good agreement with laboratory-based predictions.