Reynolds-number dependence of turbulent velocity and pressure increments

The main focus is the Reynolds number dependence of Kolmogorov normalized l ow-order moments of longitudinal and transverse velocity increments. The ve locity increments are obtained in a large number of flows and over a wide r ange (40-4250) of the Taylor microscale Reynolds number R-lambda. The R-lam bda dependence is examined for values of the separation, r, in the dissipat ive range, inertial range and in excess of the integral length scale. In ea ch range, the Kolmogorov-normalized moments of longitudinal and transverse velocity increments increase with R-lambda. The scaling exponents of both l ongitudinal and transverse velocity increments increase with R-lambda, the increase being more significant for the latter than the former. As R-lambda increases, the inequality between scaling exponents of longitudinal and tr ansverse velocity increments diminishes, reflecting a reduced influence fro m the large-scale anisotropy or the mean shear on inertial range scales. At sufficiently large R-lambda, inertial range exponents for the second-order moment of the pressure increment follow more closely those for the fourth- order moments of transverse velocity increments than the fourth-order momen ts of longitudinal velocity increments. Comparison with DNS data indicates that the magnitude and R-lambda dependence of the mean square pressure grad ient, based on the joint-Gaussian approximation, is incorrect. The validity of this approximation improves as r increases; when r exceeds the integral length scale, the R-lambda dependence of the second-order pressure structu re functions is in reasonable agreement with the result originally given by Batchelor (1951).