  Polycyclic aromatic hydrocarbons (PAHs) have been detected in numerous
circumstellar discs. We propose the continuous processing of PAHs through
clustering, adsorption on dust grains, and their reverse-processes as key
mechanisms to reduce the emission-capable PAH abundance in protoplanetary
discs. This cycle of processing is driven by vertical turbulence in the disc
mixing PAHs between the disc midplane and the photosphere. We used a
theoretical Monte Carlo model for photodesorption and a coagulation code in the
disc midplane to estimate the relevance and timescale of these processes in a
Herbig Ae/Be disc environment. By combining these components in a 1D vertical
model, we calculated the gas-phase depletion of PAHs that stick as clusters on
dust grains. Our results show that the clustering of gas-phase PAHs is very
efficient, and that clusters with more than 100 monomers can grow for years
before they are able to freeze out in the disc midplane. Once a PAH cluster is
frozen on the dust grain surface, the large heat capacity of these clusters
prevents them from evaporating off the grains in UV-rich environments such as
the photosphere. Therefore, the clustering of PAHs followed by freeze-out can
lead to a depletion of gas-phase PAHs in discs. Evaluated over the lifetime of
protoplanetary discs, we find a depletion of PAHs by a factor that ranges
between 50 and 1000 compared to the standard ISM abundance of PAHs in the inner
disc through turbulent processing. Through these processes, we favour PAHs
smaller than circumovalene as the major gas-phase emitters of the disc
photosphere as larger PAH monomers cannot photodesorb from the grain surface.
These gas-phase PAHs co-exist with large PAH clusters sticking on dust grains.
We find a close relation between the amount of PAHs frozen out on dust grains
and the dust population, as well as the strength of the vertical turbulence.
