Cavitation generates a portion of cavities called a cavitation cloud, which performs a collective unsteady motion of repeating the process of growth and collapse. In particular, it is considered that a high-pressure shock wave propagates associated with the collapse. In order to understand such unsteady behaviors of the cavitation cloud, much effort has been made for the numerical analysis of internal flows of the cavitation cloud. However, it is not clear how such a cavitation cloud can be identified as a physical entity nor how its unsteady collective motion can be elucidated in the context of the multiphase fluid flow. In this study, we make a two-dimensional numerical analysis of the multiphase flow of the submerged bubbly water jet injecting into still water through a nozzle. To model the bubbly water jet, we employ the mixture model of liquids and gases, and we utilize the Smoothed Particle Hydrodynamics method for the numerical analysis of the unsteady flows in Lagrangian description. Finally, in order to clarify the unsteady behaviors of the cloud cavitation, we show how the cavitation cloud can be generated in the context of velocity fields in the multiphase flow and in particular, we clarify how twin vortices induced by the water jet play an essential role in the expansion and shrinkage of the cloud.