This paper is associated with a poster winner of a 2019 American Physical Society's Di-vision of Fluid Dynamics (DFD) Milton van Dyke Award for work presented at the DFDGallery of Fluid Motion. The original poster is available online at the Gallery of Fluid Motion,https://doi.org/10.1103/APS.DFD.2019.GFM.P0020The 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. Examples of these applications include the atomisation of propellants in engines, the formation of droplets in injectors, mixers, separators, and the generation of droplets in multiphase flow regime transitions [2, 3, 12]. In all of these situations, it is important to predict the evolving droplet size distribution that results from a competition between breakup and coalescence, which are influenced by a range of multi-scale physics; this includes the interaction of turbulence with interfaces, capillarity, viscosity, and gravity. Therefore, it is unsurprising that the breakup of liquid jets during injection (i.e. atomisation) has received great scientific interest [4, 8, 10, 11, 13]. To the best of our knowledge, the transient dynamics of turbulent liquid/liquid systems have not been reported in the literature. Temporal instabilities and the resulting spatio-temporal interfacial structures are predicted by solving the full three-dimensional two-phase Navier-Stokes system in the context of a hybrid front-tracking/level-set method [14-16].