  It is shown that the correlation integrals (invariants) play an important,
and at certain conditions a dominant, role in helical isotropic homogeneous
turbulence both in the inertial and near-dissipation ranges. Results of direct
numerical simulations and recent laboratory experiments with multiscale grids
have been used for this purpose. A possibility of spontaneous breaking of
reflection symmetry has been also briefly discussed in this context.
