The anisotropy of the small scale structure in high Reynolds number (Rλ∼1000) turbulent shear flow

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 ${\text{100⩽R}}_{\lambda }\text{⩽1,}$ ${\text{100(6.7×10}}^2{\mathrm{⩽R}}_l{\text{⩽6.3×10}}^4\mathrm{).}$ The high $R_{\lambda }$ 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 $R_{\lambda }\mathrm{\to \infty .}$ Confirming the lower Reynolds number measurements of Garg and Warhaft [Phys. Fluids 10, 662 (1998)], we show that the skewness of $\mathrm{\partial u/\partial y}$ decreases as $R_{\lambda }^{\text{−0.5}}$ (with a value of 0.2 at $R_{\lambda }\text{∼1000).}$ Although the decrease is slower than classical scaling arguments suggest, the result is consistent with PLI, indicating a negligible value at high $R_{\lambda }.$ However, the normalized fifth moment, ${\mathrm{〈(\partial u/\partial y)}}^5{\mathrm{〉/〈(\partial u/\partial y)}}^2{〉}^{\text{5/2}},$ is of order 10, and shows no diminution with Reynolds number, while the normalized seventh moment increases with $R_{\lambda }.$ These dissipation range results are inconsistent with PLI. Within the inertial subrange we show that all the odd order moments of the increments of $\mathrm{\Delta u(y)}$ 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 $R_{\lambda }\text{∼1000,}$ and suggest it is unlikely to be so even at higher Reynolds numbers.