Three-dimensional (axisymmetric) vortices and their plane analogous generated by the impulsive or continuous action of a localized force are considered. Such structures represent a vortex ring/pair and mushroom-like flows in the form of a jet with a ring/pair at its front, respectively. Recently, the theoretical results that established a connection between flows with continuous and impulsive sources in which the outer ring radius is small, were presented. We show that the formulation of the considered problem with the arbitrary scales allows select cases when these solutions exist (in the Stokes approximations), and to transfer the obtained properties (e.g. the translation velocity) of a ring in the viscous regime to the initial regime characterized by a weak effect of viscosity. The distributions of particles in the starting ring and pair by implementing of the turbulent scales are obtained. The results from this study will be used as guidelines to examine particle transport and mixing in a vortex ring/pair that more accurately models the processes that occur in a spray combustor.