The sweeping decorrelation hypothesis and energy–inertial scale interaction in high Reynolds number flows

The random sweeping decorrelation hypothesis was analysed theoretically and experimentally in terms of the higher-order velocity structure functions Duᵢ⁽ᵐ⁾(r) = < [uᵢᵐ(x + r) - uᵢᵐ(x)]²> . Measurements in two high Reynolds number laboratory shear flows were used: in the return channel (Rλ ≈ 3.2 × 103) and in the mixing layer (Rλ ≈ 2.0 × 103) of a large wind tunnel. Two velocity components (in the direction of the mean flow, u1, and in the direction of the mean shear, u2) were processed for m = 1−4. The effect of using Taylor's hypothesis was estimated by a specially developed method, and found to be insignificant. It was found that all the higher-order structure functions scale, in the inertial subrange, as r2/3. Such a scaling has been argued as supporting evidence for the sweeping hypothesis. However, our experiments also established a strong correlation between energy- and inertial-range excitation. This finding leads to the conclusion that the sweeping decorrelation hypothesis cannot be exactly valid. The hypothesis of statistical independence of large- and small-scale excitation was directly checked with conditionally averaged moments of the velocity difference < [uᵢ(x + r) - uᵢ(x)]ˡ>uᵢ^*, l = 2-4 , at a fixed value of the large-scale parameter u*i. Clear dependence of the conditionally averaged moments on the level of averaging was found. In spite of a strong correlation between the energy-containing and the inertial-scale excitation, universality of the intrinsic structure of the inertial subrange was shown.