  The role of the moments of helicity distribution in rotating turbulence has
been studied using the notion of helical distributed chaos. Results of the
direct numerical simulations, laboratory experiments and geophysical
observations have been used in this investigation. It is shown, in particular,
that even for the cases when the global helicity is equal to zero at least even
moments are usually non-zero (due to the appearance of the local spatial
regions with strong negative and positive helicity) and can play a significant
role in the rotating turbulence as adiabatic invariants. Rotating buoyancy
driven thermal convection (Rayleigh-B\'{e}nard and Rayleigh-Taylor, the former
also for the magnetohydrodynamics) is also studied, and applications of this
approach to the convection zone of massive stars and to the geomagnetic dynamo
have been discussed in this context.
