Forced Alfvén-wave turbulence and subgrid-scale closure

The renormalization-group method is applied to the problem of forced turbulence in the simplified Alfvén model of Chen and Mahajan. The effects of small unresolvable subgrid modes on the large-scale turbulence leads to a renormalized response function ɛ. In certain limits, the resulting recursion relation for the response function can be converted into a differential equation that can be solved analytically. For Gaussian forcing terms satisfying a power-law wavenumber correlation k-^y but white-noise frequency spectrum, it is found that the response function exhibits second-harmonic generation of waves at frequency ω = 2Λv_A for all exponents y ≥ 0, where Λ is the wavenumber separating the subgrid and supergrid modes.