  We present a study of spectral laws for helical turbulence in the presence of
solid body rotation up to Reynolds numbers Re~1*10^5 and down to Rossby numbers
Ro~3*10^-3. The forcing function is a fully helical flow that can also be
viewed as mimicking the effect of atmospheric convective motions. We test in
the helical case variants of a model developed previously (Baerenzung et al.
2008a) against direct numerical simulations (DNS), using data from a run on a
grid of 15363 points; we also contrast its efficiency against a spectral Large
Eddy Simulation (LES) (Chollet and Lesieur 1981) as well as an under-resolved
DNS. The model including the contribution of helicity to the spectral eddy
dissipation and eddy noise behaves best, allowing to recover statistical
features of the flow. An exploration of parameter space is then performed
beyond what is feasible today using DNS. At fixed Reynolds number, lowering the
Rossby number leads to a regime of wave-mediated inertial helicity cascade to
small scales. However, at fixed Rossby number, increasing the Reynolds number
leads the system to be dominated by turbulent energy exchanges where the role
of inertial waves is to weaken the direct cascade of energy while strengthening
the large scales. We find that a useful parameter for partitioning the data is
NC = ReRo = U2rms/[nu Omega], with Urms, nu and Omega the rms velocity, the
viscosity and the rotation rate respectively. The parameter that determines how
much the energy cascade is direct or inverse in which case the cascade to small
scales is predominantly that of helicity is linked to Ro.
