Influence of vortex-pairing location on the three-dimensional evolution of plane mixing layers

Abstract

Detailed three-dimensional measurements of the first vortex pairing of a large plane mixing layer reveal excitation of several three-dimensional instability modes. Time evolution in three-dimensional space (x, y, z, t) shows how the two-dimensional rollers become three-dimensional as they approach each other and that the linear growth of at least two instability waves leads to a spanwise periodic pairing. The results are based on phase-locked measurements made in three-dimensional spatial grids, with a mesh spacing of 8.5% of the fundamental instability wavelength. Spanwise-uniform, periodic acoustic excitation stabilizes the most probable two-dimensional natural features – roll-up and first pairing. The second subharmonic is added to study the effect of alternate streamwise pairing locations on the three-dimensional characteristics of vortex pairing. Velocities are measured using hot-wire anemometry, and the coherent structures are reconstructed from the ensemble-averaged vorticity field.

Vortex pairing is shown to initiate through local ‘bridging’ at the maxima of periodic spanwise undulations. The undulations result from linear amplification of various instability modes on pairing rollers having different strengths. Bridging results from the change of the relative phase between the spanwise undulations of the pairing rollers from in-phase (due to the initial translative mode) to out-of-phase (due to the amplification of bulging-like and non-axisymmetric modes). It is found that when pairing occurs sufficiently far upstream, only axisymmetric waves are amplified and the evolution results in axisymmetric merging. In contrast, when pairing occurs sufficiently far downstream, both axisymmetric and non-axisymmetric waves are amplified and the evolution results in non-axisymmetric merging.

The results indicate that vortex pairing is accompanied by the counter-rotating pairs of secondary structures (‘streamwise vortices’ or ‘ribs’) located in the mixing-layer braids and residing in the valleys of the spanwise-roller waves. Time evolution of these secondary structures shows that they move in the transverse direction, following the rollers.