Pseudospectral reduction of incompressible two-dimensional turbulence

Spectral reduction was originally formulated entirely in the wavenumber domain as a coarse-grained wavenumber convolution in which bins of modes interact with enhanced coupling coefficients. A Liouville theorem leads to inviscid equipartition solutions when each bin contains the same number of modes. A pseudospectral implementation of spectral reduction which enjoys the efficiency of the fast Fourier transform is described. The model compares well with full pseudospectral simulations of the two-dimensional forced-dissipative energy and enstrophy cascades.

► Mode-reduction procedure for incompressible turbulence.
► Decimation via spectral reduction implemented with pseudospectral collocation.
► Coarse graining fast Fourier transform-based convolutions, with application to turbulent statistics.