We present a study of spectral laws for helical turbulence in the presence of solid body rotation up to Reynolds numbers Re ~ 1×10⁵ 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. (2008b)) 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 us to recover statistical features of the flow. We recall that even if the model is based on isotropic assumptions, we show in a previous study (Baerenzung et al. (2010)) that the small scales of flows at moderate Rossby number can be considered to be isotropic in the range of parameters considered here, and that, therefore, our model is appropriate to treat this kind of 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 = URMS²/ [vπ], with URMS, v and π 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.
