What does the renormalization group flow corresponding to a turbulent subrange with a broad band forcing look like?

Question

In a renormalization group analysis of turbulent flows, such as for example done by Barbi and Münster here who derive an action for the Navier-Stokes equations, insert it into the Wilson equation, and calculate the renormalization group flow numerically, scale invariant turbulent subranges corresponds to fixed points of the renormalization group flow. In particular it can be shown that Kolmogorov's scaling laws can be described by the trivial fixed point.

Phenomenologically, a scale invariant turbulent subrange can be visualized as the region of the turbulent kinetic energy (or any higher correlation function) spectrum, that lies in between a localized in wavenumber space forcing scale and a well defined dissipation scale.

If the forcing is rather broad-band instead of well localized in wavenumber space, what would the renormalization group flow corresponding to such a no longer scale invariant turbulent subrange look like?