epl draft Autocorrelation function of velocity increments 1 time series in fully developed turbulence

Abstract. In fully developed turbulence, the velocity field possesses long-range correlations, 10 denoted by a scaling power spectrum or structure functions. Here we consider the autocorrelation 11 function of velocity increment Δu`(t) at separation distance time `. Anselmet et al. [Anselmet 12 et al. J. Fluid Mech. 140, 63 (1984)] have found that the autocorrelation function of velocity 13 increment has a minimum value, whose location is approximately equal to `. Taking statistical 14 stationary assumption, we link the velocity increment and the autocorrelation function with the 15 power spectrum of the original variable. We then propose an analytical model of the autocorrelation 16 function. With this model, we prove that the location of the minimum autocorrelation function is 17 exactly equal to the separation scale time ` when the scaling of the power spectrum of the original 18 variable belongs to the range 0 < β < 2. This model also suggests a power law expression for the 19 minimum autocorrelation. Considering the cumulative function of the autocorrelation function, it 20 is shown that the main contribution to the autocorrelation function comes from the large scale part. 21 Finally we argue that the autocorrelation function is a better indicator of the inertial range than 22 the second order structure function. 23