We present a systematic analysis of the statistics of the energy dissipation rate $\epsilon$ and the enstrophy $\mathrm{\Omega }$, obtained from direct numerical simulations (DNS) of forced, incompressible turbulence in a periodic box at Taylor-scale Reynolds numbers up to $R_{\lambda }\approx 1740$. Both quantities, quadratic in the velocity-gradient tensor, are closely associated with small-scale intermittency. This paper considers the spectra of $\varphi$, the second-order correlation functions of $\varphi$, and the second-order moments of local averages of $\varphi$, where $\varphi$ denotes $\epsilon , \mathrm{\Omega }$, or their fluctuating components. The DNS results at $R_{\lambda }\approx 1100$–1740 reveal a wave-number range where the spectra scale with an exponent about $-2/3$ for both quantities. In physical space, the correlations and local averages show two scaling ranges: one with exponent about 0.23 for the total fields ($\epsilon$ and $\mathrm{\Omega }$) and another with exponent about 0.43 for their fluctuating parts. These ranges are close but not identical, and in both the correlation functions and the local averages, the total-field values are not dominated by the fluctuating parts. Under these conditions, the scaling exponents of the total and fluctuating components are unlikely to coincide, as the total includes a nonscaling mean contribution that is not negligible relative to the fluctuations. The results suggest that even at $R_{\lambda }\approx 1740$, the Reynolds number remains insufficient to reach the asymptotic regime assumed in intermittency theories.

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• Intermittency
• Turbulence
• Direct numerical simulations