The postulate of local isotropy (PLI) is tested in a wind tunnel uniform shear flow in which the Reynolds number is varied over the range 100⩽Rλ⩽1, 100(6.7×102⩽Rl⩽6.3×104). The high Rλ is achieved by using an active grid [Mydlarski and Warhaft, J. Fluid Mech. 320, 331 (1996)] in conjunction with a shear generator. We focus on the increments of the longitudinal velocity fluctuations in the direction of the mean shear. PLI requires that odd order moments of these quantities approach zero as Rλ→∞. Confirming the lower Reynolds number measurements of Garg and Warhaft [Phys. Fluids 10, 662 (1998)], we show that the skewness of ∂u/∂y decreases as Rλ−0.5 (with a value of 0.2 at Rλ∼1000). Although the decrease is slower than classical scaling arguments suggest, the result is consistent with PLI, indicating a negligible value at high Rλ. However, the normalized fifth moment, 〈(∂u/∂y)5〉/〈(∂u/∂y)2〉5/2, is of order 10, and shows no diminution with Reynolds number, while the normalized seventh moment increases with Rλ. These dissipation range results are inconsistent with PLI. Within the inertial subrange we show that all the odd order moments of the increments of Δu(y) are nonzero, exhibiting scaling ranges. Here, the skewness structure function has a value ∼0.5 indicating that in the inertial subrange significant anisotropy is evident even at the third moment level. Fifth- and seventh-order inertial subrange skewness structure functions are of order 10 and 100, respectively. The results show that PLI is untenable, both at dissipation and inertial scales, at least to Rλ∼1000, and suggest it is unlikely to be so even at higher Reynolds numbers.

The scaling exponents of the longitudinal structure function, 〈Δuxn〉 and two different transverse structure functions: the longitudinal velocity, u, measured in the transverse, y direction (the direction of the mean shear), 〈Δuyn〉, and the transverse velocity v, measured in the flow direction, x, 〈Δvxn〉, up to n=8, are studied in an approximately uniform shear flow [Shen and Warhaft, Phys. Fluids 12, 2976 (2000)], as well as in decaying (shearless) grid turbulence. Results, for low Reynolds numbers (Rλ∼100–200) and high Reynolds numbers (Rλ∼800–1000) are compared. It is shown that at high Rλ, the scaling exponents of 〈Δuyn〉, ζu(y)(n), are the same as those of the longitudinal structure function exponents, ζu(x)(n), for both even and odd values of n. The observation that ζu(y)(n)∼ζu(x)(n) (n odd) is in violation of the postulate of local isotropy (PLI) and implies that the anomalous scaling (departures from the Kolmogorov 1941 scaling) is fully captured by the anisotropy since these odd moments are zero in isotropic turbulence. In the low Rλ shear flow ζu(y)(n)<ζu(x)(n) suggesting that here this transverse component has not yet reached its high Rλ limit. In the absence of shear, ζu(y)(n)∼ζu(x)(n) at high Rλ (similar to the shear case but with the odd moments of 〈Δuyn〉 equal to zero). Similarly, at low Rλ, ζu(y)(n)<ζu(x)(n). On the other hand, the scaling exponent of the v structure function (〈Δvxn〉), ζv(x)(n), was lower than that of ζu(x)(n), even at high Rλ. The results are related to numerical, and other laboratory studies.

Structure functions to order 8 are determined from the longitudinal and transverse velocity fluctuations measured at a single point in high Reynolds number laboratory shear flow. We examine the relationship between mixed structure functions (which are explicitly zero in isotropic flow), and those of the longitudinal and transverse structure functions. Our results confirm recent findings using SO(3) symmetry decomposition [S. Kurien and K. R. Sreenivasan, Phys. Rev. E 62, 2206 (2000)] that show that the mixed structure functions have larger scaling exponents than those of the single component structure functions, i.e., the j=2 anisotropic sector structure function scaling exponent is greater than that of the j=0 isotropic sector. However, we also show that the ratio of the j=2 to j=0 sector scaling exponents systematically decreases with increasing order, suggesting that at higher orders there is persistence of anisotropy at the smallest scales. Difficulties in the analysis due to the difference in scaling exponents of the transverse and longitudinal structure functions are addressed.

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