  Invariance properties of physical systems govern their behavior: energy
conservation in turbulence drives a wide distribution of energy among modes,
observed in geophysical or astrophysical flows. In ideal hydrodynamics, the
role of helicity conservation (correlation between velocity and its curl,
measuring departures from mirror symmetry) remains unclear since it does not
alter the energy spectrum. However, with solid body rotation, significant
differences emerge between helical and non-helical flows. We first outline
several results, like the energy and helicity spectral distribution and the
breaking of strict universality for the individual spectra. Using massive
numerical simulations, we then show that small-scale structures and their
intermittency properties differ according to whether helicity is present or
not, in particular with respect to the emergence of Beltrami-core vortices
(BCV) that are laminar helical vertical updrafts. These results point to the
discovery of a small parameter besides the Rossby number; this could relate the
problem of rotating helical turbulence to that of critical phenomena, through
renormalization group and weak turbulence theory. This parameter can be
associated with the adimensionalized ratio of the energy to helicity flux to
small scales, the three-dimensional energy cascade being weak and self-similar.
