The random sweeping decorrelation hypothesis was analysed theoretically and experimentally in terms of the higher-order velocity structure functions $D_{u_i}^{(m)}(r) = \left< [u_i^m(x + r) - u_i^m(x)]^2\right>$. 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 $\left< [u_i(x + r) - u_i(x)]^l\right>_{u_i^*}, l = 2-4$, 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.

In the present paper we obtain a theoretical expression for the temperature fluctuation spectrum for a Prandtl number of approximately one and for the region where both viscosity and molecular heat conductivity are important. An asymptotic theory for very large wavenumbers of the temperature spectrum in the turbulent flow is developed. The assumption of smallness of the correlation coefficient between the product of small-scale components of velocities at two points and the corresponding product of small-scale components of temperatures is used. The results of simultaneous measurements of streamwise velocity fluctuations and temperature fluctuations carried out in the plane of symmetry of a two-dimensional wake behind a slightly heated cylinder (Rλ = 270) in a wind tunnel is consistent with this assumption.The main result of the theory developed is the appearance of a bump in the temperature spectrum for a Prandtl number of approximately one.

The fractal properties of isovelocity surfaces are studied in three high Reynolds number (Rλ≊2.0×102–3.2×103) laboratory shear flows using the standard box-counting method. The fractal dimension D=−d(log Nr)/d(log r) was estimated within the range of box sizes r from several Kolmogorov scales up to several integral scales (Nr is the number of boxes with size r required to cover the line intersection of an isovelocity surface). The inertial subrange was of particular interest in this investigation. Measurements were carried out for external intermittency factors γ≊0.6–1.0. The data were processed using threshold levels U±2.5u′ (U and u′ denote mean and rms values of longitudinal velocity). Over the parameters studied, no wide range of constant fractal dimension was found. On the other hand, the accuracy of constant fractal dimension approximation with D≊0.4 over the inertial subranges was shown to be similar to that of the Kolmogorov [Dokl. Akad. Nauk SSSR 30, 301 (1941)] ‘‘two-thirds law.’’

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