Analysis of simple turbulence models by means of the amplitude equation

The Navier-Stokes equation written in Fourier transforms (the so-called amplitude equation) is applied to the analysis of spectral energy transfer processes in individual realizations of two-dimensional turbulent flow fields. Mathematical models are proposed for flows free of spectral energy transfer. It is shown that in isolated isotropic realizations of two-dimensional flow fields, spectral energy transfer is absent.