Laboratory observations of secondary structures in kelvin-helmhoitz billows and consequences for ocean mixing

Abstract

Experiments have been made using shadowgraphs to examine the development of secondary structures in Kelvin-Helmhoitz billows at the diffuse interface between two layers of different densities moving in shear at moderate Reynolds numbers and high Prandtl number. The onset of turbulence in billows reported in earlier work resulted from an interaction between the billows and the side walls of the apparatus. Secondary structure within the billows remote from the side walls occurs later and is, in its early stages, well organised. Regular longitudinal bands lying parallel to the mean flow develop near the vertical boundaries of the billows and extend across their widths. The initial development and scale of the spanwise bands are similar to that of the convective rolls predicted to occur in billows by Klaassen and Peltier (1985a) using a numerical model. No longitudinal instability is observed to occur at the same time in the braids between the billows. Fine scale “turbulence” occurs in the billows about one stability period (for the original interface) after the secondaries first appear, so that the transition is not, as previously thought, “explosive” but is relatively slow. Two other “transitional” structures are reported. One has a tube-like appearance extending from one billow to its neighbour. Disturbances are transmitted down the tube and these ultimately initiate turbulence in the second billow. The second structure is a “knot” due to the spanwise amalgamation of two-billows into one. The relevance of the observations to geophysical flows is discussed. Earlier estimates of the efficiency of mixing due to Kelvin-Helmhoitz instability are put into doubt. Billows typical of those observed by Woods (1968) in the oceanic seasonal thermocline should develop secondary bands at a scale of about 2 cms.