The pulse detonation engine (PDE) has the potential to drastically increase the efficiency of conventional gas turbines, which currently contain isobaric combustors. In a hybrid-PDE configuration, these combustors are replaced by an annular array of pulse detonation combustors (PDCs). Each PDC consists of a pipe containing a convergent-divergent nozzle that is filled with a stoichiometric mixture of hydrogen and air. Ignition of the mixture results in an accelerating deflagration (subsonic combustion wave), forming a leading shock wave that focuses at the convergent-divergent nozzle to produce a detonation (supersonic combustion wave). This process is demonstrated using a 2D numerical simulation and reveals the essential aspects of the detonation transition. The detonation travels through the PDC detonation tube before exhausting out of the open end and producing a transient supersonic jet. This transient exhaust flow is visualized using the schlieren technique, highlighting the changes in the density gradient. By altering the PDC's operating conditions, the underlying fluid dynamic process of the transient supersonic jet is visualized in great detail. Alongside the scientific insights, the visualizations show the complexity and beauty associated with the dynamic evolution of a transient supersonic jet.