  Intermittency is one of central obstacles for understanding small-scale
dynamics in the fully developed hydrodynamic turbulence. The modern approach is
largely based on the multifractal theory of Parisi and Frisch which is,
however, phenomenological. It was shown recently that the intermittency can be
related to the hidden scale invariance. The latter is a new statistical scaling
symmetry unbroken in a rescaled (projected) formulation of equations of motion.
In the present work, we consider a shell model of turbulence and describe how
the hidden symmetry manifests itself through all scales, both in the inertial
interval and in the transition to forcing and dissipation ranges. In the
inertial interval, we derive anomalous scaling laws from the hidden symmetry.
Then, we show how a complicated form of the dissipation range is controlled by
intermittent rescaled Reynolds numbers within a large range of dissipation
scales. This dissipative intermittency can be removed by using a special class
of dissipation models. For such models, the hidden scale invariance is restored
both in the inertial interval and the dissipation range. Overall, the presented
approach deduces the multifractal theory and some of its basic conclusions from
the hidden scaling symmetry of equations of motion.
