Finite Reynolds number effect on the scaling range behaviour of turbulent longitudinal velocity structure functions
Résumé
The effect of large-scale forcing on the second- and third-order longitudinal velocity structure functions, evaluated at the Taylor microscale r A. is assessed in various turbulent flows at small to moderate values of the Taylor microscale Reynolds number RA. It is found that the contribution of the large-scale terms to the scale by scale energy budget differs from flow to flow. For a fixed RA, this contribution is largest on the centreline of a fully developed channel flow but smallest for stationary forced periodic box turbulence. For decaying-type flows, the contribution lies between the previous two cases. Because of the difference in the large-scale term between flows, the third-order longitudinal velocity structure function at r = A differs from flow to flow at small to moderate RA. The effect on the second-order velocity structure functions appears to be negligible. More importantly, the effect of RA on the scaling range exponent of the longitudinal velocity structure function is assessed using measurements of the streamwise velocity fluctuation ii, with RA in the range 500-1100, on the axis of a plane jet. It is found that the magnitude of the exponent increases as RA increases and the rate of increase depends on the order ii. The trend of published structure function data on the axes of an axisymmetric jet and a two-dimensional wake confirms this dependence. For a fixed RA, the exponent can vary from flow to flow and for a given flow, the larger RA is, the closer the exponent is to the value predicted by Kolmogorov (Dok!. Akad. Nauk SSSR, vol. 30, 1941a, pp. 299-303) (hereafter K41). The major conclusion is that the finite Reynolds number effect, which depends on the flow, needs to he properly accounted for before determining whether corrections to K41, arising from the intermittency of the energy dissipation rate, are needed. We further point out that it is imprudent, if not incorrect, to associate the finite Reynolds number effect with a consequence of the modified similarity hypothesis introduced by Kolmogorov (J. Fluid Mech., vol. 13, 1962, pp. 82-85) (K62); we contend that this association has misled the vast majority of post K62 investigations of the consequences of K62.