  Airy beams are solutions to the paraxial Helmholtz equation known for
exhibiting shape invariance along their self-accelerated propagation in free
space. These two properties are associated with the fact that they are not
square integrable, that is, they carry infinite energy. To circumvent this
drawback, families of so-called finite-energy Airy-type beams have been
proposed in the literature and, in some cases, also implemented in the
laboratory. Here an analysis of the propagation of this type of structured
light beams is presented from a flux trajectory perspective with the purpose to
better understand the mechanisms that make infinite and finite energy beams to
exhibit different behaviors. As it is shown, while the foremost part of the
beam can be clearly and unambiguously associated with the well-known
accelerating term, the rear part of the beam corresponds to a nearly
homogeneous distribution of flow trajectories, particularly for large
propagation distances. This is shown to be related with an effective transfer
of trajectories between adjacent lobes (gradually, from the fore part of the
beam to its rear part), which leads to smearing out the transverse flow along
the rear part of the beam. This is sharp contrast with the situation found in
ideal Airy beams, where trajectories belonging to a given lobe of the intensity
distribution remain the same all along the propagation. The analysis is
supplemented with an also trajectory-based description of Young's experiment
performed with finite-energy Airy beams in order to provide a dynamical
understanding of the autofocusing phenomenon observed with circular Airy beams.
