  Skewness and non-Gaussian behavior are essential features of the distribution
of short-scale velocity increments in isotropic turbulent flows. Yet, although
the skewness has been generally linked to time-reversal symmetry breaking and
vortex stretching, the form of the asymmetric heavy tails remain elusive. Here
we describe the emergence of both properties through an exactly solvable
stochastic model with a scale hierarchy of energy transfer rates. From a
statistical superposition of a local equilibrium distribution weighted by a
background density, the increments distribution is given by a novel class of
skewed heavy-tailed distributions, written as a generalization of the Meijer
$G$-functions. Excellent agreement in the multiscale scenario is found with
numerical data of systems with different sizes and Reynolds numbers.
Remarkably, the single scale limit provides poor fits to the background
density, highlighting the central role of the multiscale mechanism. Our
framework can be also applied to describe the challenging emergence of skewed
distributions in complex systems.
