Longitudinal and transverse structure functions in sheared and unsheared wind-tunnel turbulence

Abstract

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.