the form of a vorticity equation in which the forcing and dissipation term, instead of being localized respectively at large and small scales, act over the whole of the inertial range, and this is reflected in their being nonlocal operators in real space. This is opposite to what happens in a real turbulent field, where energy balance is established between large scale forcing and small scale viscous dissipation, by means of the nonlinear cascade. A nonlinear cascade is still present because of the convection term, but it acts on the timescale of the eddy turn-over time, and, for large $\rho$, its effect is only a correction to that of the forcing and damping terms. Choosing $\rho$ large has therefore the consequence that convection acts merely as a large scale sweep.

Actually, Eqn. (2.7) looks a lot like the typical starting point of many turbulent closures [@kraichnan71; @orszag77; @yakhot86], in which $\gamma_k$ gives the turbulent response function (eddy viscosity of small scales) and $h_k$ the nonlinear forcing by the cascade. For instance, $\rho^{-2}$ coincides with the renormalized dimensionless coupling constant of the Renormalization Group (RNG) closure [@yakhot86; @olla91], and its smallness is there the basis for the establishment of a perturbation 