Reynolds number dependence of moments of kinetic energy dissipation rate and enstrophy

Probability density functions (PDFs) of the kinetic energy dissipation rate and enstophy have recently been found to be stretched gamma distribution with the same stretching exponents. The prefactor of the exponential function is of the power law with the exponents 3/2 and 1/2 for the dissipation and enstrophy, respectively, that are known from the Gaussian random velocity. Under the constraints of the normalization and unity for the mean on the PDF, it is theoretically predicted that the moments of the order between 0 and 1 decrease with increase of the Reynolds number, while those with the order lower than 0 or greater than 1 increase with the Reynolds number. A set of the direct numerical simulation (DNS) confirms this trend of the moments. Implication of the Reynolds number dependence of these moments on the spectra of the kinetic energy and scalar variance will be discussed.