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.