Inertial-range intermittency and accuracy of direct numerical simulation for turbulence and passive scalar turbulence

Abstract

We examine the effects of the variation in dissipation-range resolution on the accuracy of inertial-range statistics and intermittency in terms of the direct numerical simulations of homogeneous turbulence and passive-scalar turbulence by changing the spatial resolution up to 20483 grid points while maintaining a constant Reynolds number at Rλ ≃ 180 or ≃ 420 and Schmidt number at Sc = 1. Although large fluctuations of the derivative fields depended strongly on Kmaxη and were underestimated when Kmaxη≃1, where Kmax is the maximum wavenumber in the computations and η is the mean Kolmogorov length, the behaviour of the spectra and the scaling exponents of the structure functions up to the eighth order in the range of scales greater than 10η was insensitive to variations in Kmaxη, even when Kmaxη≃1. The relationship between the spatial resolution and asymptotic tail of the probability density functions of the energy dissipation fields was studied using the multifractal model for dissipation, and the results were confirmed by comparison to the simulation data. Degradation of the statistics arises from modifications to the flow dynamics due to the finite wavenumber cutoff and the use of a coarser filter width for the data, which is obtained using a reasonable accuracy criterion for the flow dynamics. The effect of the former was less than that of the latter for the low-to-moderate-order statistics when Kmaxη≥1. We also discuss the universality of the inertial-range statistics with respect to variations in the dissipation-range characteristics.