Initial streamwise vorticity formation in a two-stream mixing layer

Abstract

The characteristics of the initial formation of streamwise vortices and their relation to the spanwise structures are experimentally investigated at several phases of the initial roll-up and pairing in a two-stream mixing layer at high Reynolds numbers (up to Reθ = 1.25 × 103). The spanwise structures were stabilized by acoustically exciting the mixing layer at the natural instability frequency and its first subharmonic. No artificial spanwise forcing was applied. Quantitative information was obtained through conditional sampling with the forcing signal as the phase reference. Time traces of the three velocity components were recorded by hot-wire anemometry at a grid of locations on planes normal to the flow at four successive streamwise locations which include the roll-up and first pairing of the spanwise structures. From these measurements, three-dimensional distributions of ensemble-average vorticity components were computed and analysed.The results show that the spanwise structures remain mostly two-dimensional from roll-up to the end of the first pairing, except for small oscillations in curvature of their axes. Concentrated streamwise vortices evolve at locations corresponding to small ‘kinks’ in the spanwise rollers and first appear at the beginning of the pairing process. Their subsequent development bears many similarities with the results of small-perturbation simulations. They expand laterally, forming counter-rotating rib vortices that grow almost exponentially in the braid region. In the core region, a complex but organized streamwise vorticity pattern emerges. The pattern consists of layered streamwise vortices whose orientation suggests that the oscillation of the spanwise roller core is π radians out of phase with that of the streamwise vortex lines that join the rib vortices. The peak streamwise vorticity and circulation in the core region increase until the completion of the spanwise structure pairing when the layered pattern collapses. Measurements at large spanwise locations conducted downstream show that the ‘kink’ is not the only location of streamwise vorticity generation: streamwise vortices develop at nearly periodic spanwise locations other than that of the initial ‘kink’. The initial spacing between streamwise vortices agrees with previous stability analysis. At the end of the spanwise structure pairing, isolated pairings between streamwise vortices take place, but a global doubling in spanwise wavelength does not occur.