Spectral reduction: a statistical description of turbulence

Details Spectral reduction: a statistical description of turbulence Spectral reduction: a statistical description of turbulence

1999-03-05

arxiv.org/abs/chao-dyn/9903008v4

Nonlinear Sciences

Chaotic Dynamics

12 pages, 4 figures, to appear in Physical Review Letters

Scientific paper

10.1103/PhysRevLett.83.5491

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.

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