  Multifractal systems usually have singularity spectra defined on bounded sets
of H\"older exponents. As a consequence, their associated multifractal scaling
exponents are expected to depend linearly upon statistical moment orders at
high enough orders -- a phenomenon referred to as the {\it{linearization
effect}}. Motivated by general ideas taken from models of turbulent
intermittency and focusing on the case of two-dimensional systems, we
investigate the issue within the framework of Gaussian multiplicative chaos. As
verified by means of Monte Carlo simulations, it turns out that the
linearization effect can be accounted for by Liouville-like random measures
defined in terms of upper-bounded scalar fields. The coarse-grained statistical
properties of Gaussian multiplicative chaos are furthermore found to be
preserved in the linear regime of the scaling exponents. As a related
application, we look at the problem of turbulent circulation statistics, and
obtain a remarkably accurate evaluation of circulation statistical moments,
recently determined with the help of massive numerical simulations.
