The interaction of initially isolated jets arises in a wide range of engineering applications, including cooling devices, combustors, and fuel injectors. Many previous investigations of such applications have focused primarily on how the jet interactions affect time-averaged flow and turbulence characteristics. However, the dynamical processes underlying these interactions have remained largely unexplored, leading to potential uncertainty regarding the performance and optimization of engineering systems. In this study, we explore interacting jet dynamics through highly resolved simulations of two turbulent interacting slot jets. We use adaptive mesh refinement to add resolution to the simulations only in the regions of interest. We perform proper orthogonal decomposition and dynamic mode decomposition on the region where the four shear layers associated with the initially separate jets merge and transition into a single jet stream. These decompositions allow us to distinguish between the different types of vortex shedding that occur, as well as to demonstrate the irregularity of the jet merging process.