  The breakup of an interface into a cascade of droplets and their subsequent
coalescence is a generic problem of central importance to a large number of
industrial settings such as mixing, separations, and combustion. We study the
breakup of a liquid jet introduced through a cylindrical nozzle into a stagnant
viscous phase via a hybrid interface-tracking/level-set method to account for
the surface tension forces in a three-dimensional Cartesian domain. Numerical
solutions are obtained for a range of Reynolds (Re) and Weber (We) numbers. We
find that the interplay between the azimuthal and streamwise vorticity
components leads to different interfacial features and flow regimes in Re-We
space. We show that the streamwise vorticity plays a critical role in the
development of the three-dimensional instabilities on the jet surface. In the
inertia-controlled regime at high Re and We, we expose the details of the
spatio-temporal development of the vortical structures affecting the
interfacial dynamics. A mushroom-like structure is formed at the leading edge
of the jet inducing the generation of a liquid sheet in its interior that
undergoes rupture to form droplets. These droplets rotate inside the mushroom
structure due to their interaction with the prevailing vortical structures.
Additionally, Kelvin-Helmholtz vortices that form near the injection point
deform in the streamwise direction to form hairpin vortices, which, in turn,
trigger the formation of interfacial lobes in the jet core. The thinning of the
lobes induces the creation of holes which expand to form liquid threads that
undergo capillary breakup to form droplets.
