Spectral reduction: A statistical description of turbulence

A method is described for predicting statistical properties of turbulence. Collections of Fourier amplitudes are represented by nonuniformly spaced modes with enhanced coupling coefficients. The statistics of the full dynamics can be recovered from the time-averaged predictions of the reduced model. A Liouville theorem leads to inviscid equipartition :solutions. Excellent agreement is obtained with two-dimensional forced-dissipative pseudospectral simulations. For the two-dimensional enstrophy : cascade, logarithmic corrections to the high-order structure:functions are observed.