Vortex pairing : the mechanism of turbulent mixing-layer growth at moderate Reynolds number

TLDR

A mixing layer is created by two water streams of different velocities in a lucite‑walled channel, with Reynolds numbers ranging from about 45 at the origin to roughly 850 after 50 cm. By injecting dye between the streams, the authors track vorticity and model the layer’s growth using the non‑uniformity of the vortex train and the lumpiness of the vorticity field as key controlling factors. Unstable waves roll up into discrete two‑dimensional vortices that repeatedly pair, producing larger structures with twice the spacing and thereby governing the mixing‑layer growth.

Abstract

A mixing layer is formed by bringing two streams of water, moving at different velocities, together in a lucite-walled channel. The Reynolds number, based on the velocity difference and the thickness of the shear layer, varies from about 45, where the shear layer originates, to about 850 at a distance of 50 cm. Dye is injected between the two streams just before they are brought together, marking the vorticity-carrying fluid. Unstable waves grow, and fluid is observed to roll up into discrete two-dimensional vortical structures. These turbulent vortices interact by rolling around each other, and a single vortical structure, with approximately twice the spacing of the former vortices, is formed. This pairing process is observed to occur repeatedly, controlling the growth of the mixing layer. A simple model of the mixing layer contains, as the important elements controlling growth, the degree of non-uniformity in the vortex train and the ‘lumpiness’ of the vorticity field.