From hot-wire anemometer measurements in active-grid wind-tunnel turbulence we have determined the Reynolds number dependence of the velocity derivative moments, the mean-squared pressure gradient, χ , and the normalized acceleration variance, a₀ , over the Reynolds number range 100\,≤\,R_λ\,≤\,900 . The values of χ and a₀ were obtained from the fourth-order velocity structure functions. The derivative moments show power-law dependence on Reynolds number and the exponent is the same with or without shear. In particular, we find the derivative kurtosis, K∂ u/∂ x\,~\,R_λ0.39 , and there is no evidence of the transition that has been observed in this quantity in some recent work. We find that at high Reynolds numbers, χ and a₀ tend to values similar to those obtained by direct particle tracking measurements and by direct numerical simulation. However, at lower Reynolds number our estimates of χ and a₀ appear to be affected by the evaluation technique which imposes strict requirements on local homogeneity and isotropy.
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Gylfason et al. (2004) studied this question.