A generalization to the transient regime is developed for waves with a phase singularity of the screw type. These singular waves are ommonly called vortices for all kind of waves as for instance, optical vortex or acoustical vortex. We generalize the definition of vortices to get an azimuthal velocity invariant for all the frequency components contained in the broad spectrum of a short pulse. This generalization leads to a modification of the orbital angular momentum definition. Another generalization is introduced by considering helicoidal waves with a finite number of turns. We demonstrate that in this last case, the topological charge is no longer an integer. This provides a physical interpretation to vortices of fractional charge that are here involved to take into account the diffraction occurring at both tips of the now finite helical wavefront. We show that shortening the pulse implies an angular localization of the wave energy and as a onsequence, a spreading of the angular momentum amplitude due to the uncertainty principle.