The effect of Reynolds number on mixing in Kelvin–Helmholtz billows

Abstract

AbstractMixing induced through the life-cycle of Kelvin–Helmholtz (KH) billows is studied for a range of low and intermediate Reynolds numbers using direct numerical simulations (DNS). The amount of stirring, and therefore mixing, is significantly controlled by the process of vortex pairing of two KH billows. For low Reynolds numbers, vortex pairing of the billows is complete in the pre-turbulent stage or early stages of turbulence, generating a high amount of stirring. At higher Reynolds numbers, vortex pairing is suppressed by the growth of three-dimensional instabilities, and the amount of stirring is significantly reduced. For single KH billows, as the Reynolds number increases, there is a transition in the characteristics of the mixing, similar to the laboratory measurements of Breidenthal (J. Fluid Mech., vol. 109, 1981, pp. 1–24) and Koochesfahani & Dimotakis (J. Fluid Mech., vol. 170, 1986, pp. 83–112). The transition in mixing is associated with the growth and sustainability of three-dimensional motions at sufficiently high Reynolds numbers. We examine this ‘mixing transition’ and the influence of vortex pairing on it by examining the flow properties at different stages and the exchange between the energy partitions. As the Reynolds number increases, three-dimensional motions develop over a wider range of length scales, and smaller scale eddies form. However, this does not necessarily result in a greater amount of mixing. The maximum total amount of mixing induced over the lifetime of a KH instability, for billows both with and without vortex pairing, occurs when the large-scale eddies that cause the stirring are the most energetic. The mixing efficiency reveals a non-monotonic dependence on the Reynolds number.