To understand further the mixing process between the injected fuel and air in the combustion chamber of a diesel engine, the turbulent mixing process in a one-phase, two-dimensional transient jet was theoretically studied using the discrete vortex simulation. First, the simulation model was evaluated by comparisons between calculated and experimental data on two-dimensional turbulent jets. Second, the trajectories of the injected fluid elements marked with different colors were graphically demonstrated. Also the process of entrainment of the surrounding fluid into the jet was visually presented using colored tracers. Major results obtained are; 1) the fluid elements injected at the early stage of injection period are pushed forward by succeeding elements, and turn round at the jet tip being involved in a pair of large vortices formed in the jet head, and 2) the surrounding fluid is entrained into the jet through a number of crevices formed by vortices on the jet boundary, and the entrainment scarcely occurs in the jet head.