  We analyze the isotropic component of turbulent flows spanning a broad range
of Reynolds numbers. The aim is to identify scaling laws and their Reynolds
number dependence in flows under different mechanical forcings. To this end, we
applied an SO(3) decomposition to data stemming from direct numerical
simulations with spatial resolutions ranging from 64^3 to 1024^3 grid points,
and studied the scaling of high order moments of the velocity field. The study
was carried out for two different flows obtained forcing the system with a
Taylor-Green vortex or the Arn'old-Beltrami-Childress flow. Our results
indicate that helicity has no significant impact on the scaling exponents.
Intermittency effects increase with the Reynolds number in the range of
parameters studied, and are larger than what can be expected from several
models in the literature. Finally, we confirm previous results showing the use
of the SO(3) decomposition improves the convergence of scaling exponents.
