The results of numerical simulation of the formation and motion of turbulent puffs resulting from the blowing of pulsed jets with different initial velocities and durations are presented. A model of an axisymmetric turbulent flow described by non-stationary Reynolds equations is adopted. It is shown that, regardless of the initial conditions, after the same dimensionless time interval from the instant the jet outflow begins, a vortex cloud appears, which has a spherical shape of vortex. The vortex-induced flow in the rest of the space is close to potential. It has been established that the velocity profiles in vortices in the axial and transverse directions are close to self-similar and are similar for different conditions of the outflow of pulsed jets. Time dependences of the geometric and kinematic characteristics of puffs are presented and analyzed: the position of the cloud center (points with maximum velocity) and the radius of a sphere equivalent in volume to a puff, as well as maximum and average velocities. For the studied jet outflow conditions, the characteristics of puffs turn out to be similar.