  We study the morphology of Eulerian vortical structures and their interaction
with density interfaces in increasingly turbulent stably-stratified shear
layers. We analyse the three-dimensional, simultaneous velocity and density
fields obtained in the stratified inclined duct laboratory experiment. We
track, across 15 datasets, the evolution of coherent structures from
pre-turbulent Holmboe waves, through intermittent turbulence, to full
turbulence and mixing. We use the Rortex--Shear decomposition of the vorticity
field into a pure rotational part (the rortex vector), and a non-rotational
part (the shear vector). We describe the morphology of ubiquitous hairpin-like
vortical structures (revealed by the rortex), similar to those commonly
observed in boundary-layer turbulence. These are born as relatively weak
vortices around the strong three-dimensional shearing structures of confined
Holmboe waves, and gradually strengthen and deform under increasing turbulence,
transforming into pairs of upward- and downward-pointing hairpins propagating
in opposite directions on the top and bottom edge of the shear layer. Each
hairpin's pair of legs are counter-rotating and entrain fluid laterally and
vertically, and their arched-up `heads', which are transverse vortices, entrain
fluid vertically. We then elucidate how this large-scale vortex morphology
stirs and mixes the density field. Essentially, vortices located at the sharp
density interface on either edge of the mixing layer (mostly hairpin heads)
engulf blobs of unmixed fluid into the mixing layer, while vortices inside the
mixing layer (mostly hairpin legs) further stir it, generating strong,
small-scale shear, enhancing mixing. These findings provide new insights into
the role of turbulent coherent structures in shear-driven stratified mixing.
