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

The scaling exponents of the longitudinal structure function, < Deltau(x)(n)> and two different transverse structure functions: the longitudinal velocity, u, measured in the transverse, y direction (the direction of the mean shear), < Deltau(y)(n)>, and the transverse velocity v, measured in the flow direction, x, < Deltav(x)(n)>, 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 (R(lambda)similar to 100-200) and high Reynolds numbers (R(lambda)similar to 800-1000) are compared. It is shown that at high R-lambda, the scaling exponents of < Deltau(y)(n)>, zeta (u(y))(n), are the same as those of the longitudinal structure function exponents, zeta (u(x))(n), for both even and odd values of n. The observation that zeta (u(y))(n)similar to zeta (u(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 R-lambda shear flow zeta (u(y))(n)< zeta (u(x))(n) suggesting that here this transverse component has not yet reached its high R-lambda limit. In the absence of shear, zeta (u(y))(n)similar to zeta (u(x))(n) at high R lambda (similar to the shear case but with the odd moments of < Deltau(y)(n)> equal to zero). Similarly, at low R-lambda, zeta (u(y))(n)< zeta (u(x))(n). On the other hand, the scaling exponent of the v structure function (< Deltav(x)(n)>), zeta (v(x))(n), was lower than that of zeta (u(x))(n), even at high R-lambda. The results are related to numerical, and other laboratory studies. (C) 2002 American Institute of Physics.