  An optical vortex beam propagating through turbulent atmosphere encounters
distortions in the wavefront that results in modal scattering. Abruptly
autofocussing (AAF) beams with orbital angular momentum have gained significant
attention due to their non-diffracting and self-healing nature. These warrants
understanding of the behaviour of these beams through turbulent atmosphere
absolutely necessary. With this intuition, in the present work we investigate
the behaviour of two AAF beams namely ring Airy vortex beam (RAVB) and ring
Pearcey vortex beam (RPVB) through the turbulent atmosphere in two cases:
multiplexed and non-multiplexed. We propagate multiplexed as well as
non-multiplexed RAVB and RPVB in different levels of turbulent atmosphere. In
non-multiplexed case, channel efficiency declines for both the beams with
increase in modes numbers. In multiplexed case, increasing the gap between the
mode sets results in decrease in channel efficiency. We also report that in
weak atmospheric turbulence RAVB outperform RPVB in terms of channel
efficiency. We use optical transformation sorting (log-polar) method to
demultiplex the optical beams at the output. Furthermore, we investigate and
compare the OAM spectra of both beams in different levels of atmospheric
turbulence and at different propagation distances. The comparison reveals that
the spectra of RPVB is more dispersive as compared to that of RAVB.
