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In fully developed turbulence, the velocity field possesses long-rangecorrelations, denoted by a scaling power spectrum or structure functions. Herewe consider the autocorrelation function of velocity increment $ {\Deltau_{\ell}(t)}$ at separation {time} $\ell$. Anselmet et al. [Anselmet et al. J.Fluid Mech. \textbf{140}, 63 (1984)] have found that the autocorrelationfunction of velocity increment has a minimum value, whose location isapproximately equal to $\ell$. Taking statistical stationary assumption, welink the velocity increment and the autocorrelation function with the powerspectrum of the original variable. We then propose an analytical model of theautocorrelation function. With this model, we prove that the location of theminimum autocorrelation function is exactly equal to the separation {time}$\ell$ when the scaling of the power spectrum of the original variable belongsto the range $0<\beta<2$. This model also suggests a power law expression forthe minimum autocorrelation. Considering the cumulative function of theautocorrelation function, it is shown that the main contribution to theautocorrelation function comes from the large scale part. Finally we argue thatthe autocorrelation function is a better indicator of the inertial range thanthe second order structure function.

Autocorrelation function of velocity increments time series in fully developed turbulence