Evolution of a quasi-two-dimensional shear layer in a soap film flow

Abstract

A quasi-two-dimensional shear layer is produced by merging two gravity-driven flows of soap film at different average velocities. The Kelvin–Helmholtz instability dominates the evolution of the shear layer, similar to what is observed in three-dimensional shear layers. However, the constraints that effectively limit the flow to two spatial dimensions have a considerable influence on the development of secondary instabilities and transition to turbulence. Nearly 40 cm downstream in the flow, two two-dimensional instabilities are observed, namely, vortex-pairing and secondary Kelvin–Helmholtz instability. The development of secondary instabilities and transition to turbulence in the flow is also affected by the interaction of the flowing soap film with boundary layers forming in the air surrounding the flowing soap film in the direction normal to the plane of the film. This becomes apparent when the flow is analyzed quantitatively in terms of the mixing interface length and fractal dimension. Initially, the mixing interface length grows exponentially with the downstream distance; however, beyond a certain distance, the growth stops. For the fractal dimension of the mixing interface in our quasi-two-dimensional shear layer, we have observed a peak value of 1.27 as compared to 1.34 reported in the literature for a corresponding section of a three-dimensional shear layer. For scales larger than ∼1 cm, interaction with air begins to dominate as the leading mechanism of dissipation. Coupling with boundary layers in air near the soap film drains energy from the large flow features and apparently “freezes” its evolution, producing “fossil” turbulence at large downstream distances.