Reynolds-number dependence of turbulent velocity and pressure increments

Abstract

The main focus is the Reynolds number dependence of Kolmogorov normalized low-order moments of longitudinal and transverse velocity increments. The velocity increments are obtained in a large number of flows and over a wide range (40–4250) of the Taylor microscale Reynolds number R_λ. The R_λ dependence is examined for values of the separation, r, in the dissipative range, inertial range and in excess of the integral length scale. In each range, the Kolmogorov-normalized moments of longitudinal and transverse velocity increments increase with R_λ. The scaling exponents of both longitudinal and transverse velocity increments increase with R_λ, the increase being more significant for the latter than the former. As R_λ increases, the inequality between scaling exponents of longitudinal and transverse velocity increments diminishes, reflecting a reduced influence from the large-scale anisotropy or the mean shear on inertial range scales. At sufficiently large R_λ, 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 moments of longitudinal velocity increments. Comparison with DNS data indicates that the magnitude and R_λ dependence of the mean square pressure gradient, 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_λ dependence of the second-order pressure structure functions is in reasonable agreement with the result originally given by Batchelor (1951).