Non-Gaussian statistics in isotropic turbulence

Several measures of non-Gaussian behavior in simulations of decaying isotropic turbulence are compared with predictions of the direct-interaction approximation (DIA) at an initial Rλ∼35. The quantities studied include the variances and wavenumber power spectra of (a) the total nonlinear term in the Navier--Stokes equation, (b) the time derivative of the velocity at a point, (c) pressure fluctuations, and (d) vorticity and dissipation fluctuations. The direct-interaction approximation gives a good quantitative prediction of the variance of the time derivative and the variance of total nonlinear term, and a fair qualitative prediction of the power spectrum associated with the latter. But DIA totally fails to capture the non-Gaussian statistics associated with pressure fluctuation and vorticity spottiness. Some discussion is given of demands that vorticity and dissipation statistics place upon theories of tubulence at moderate and high Reynolds numbers