The dynamic model of Canuto and Dubovikov was designed to describe fully developed turbulence which also corresponds to our study.

A family of models was developed to describe the nonlinear interactions in spectral space for an incompressible homogeneous turbulence (DIA, TFM, EDQNM, ...). More recently, the dynamic model of Canuto and Dubovikov has also been developed in the context of spectral representation of nonlinear mechanisms.

In its design, the dynamic model of Canuto and Dubovikov is based  on Wyld equations [1] which are exact formal solutions of the Navier-Stokes equations. These equations lead to represent the nonlinear interactions through two mechanisms leading force  in charge of a turbulent flow of energy  and a dependent viscosity  in spectral space wave vector  Through the theory of renormalization group (RNG), p and  are expressed using infinite series p. Finally, the series giving p contain like (IR) divergences that are not renormalizable, and to express p, the dynamic model of Canuto and Dubovikov uses the concept of energy locality [1-5].

homogeneous turbulence, dynamic model, two-dimensional turbulence, enstrophy, palinstrophy.