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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.