Towards local isotropy of higher-order statistics in the intermediate wake
Résumé
In this paper, we assess the local isotropy of higher-order statistics in the intermediate wake region. We focus on normalized odd moments of the transverse velocity derivatives, M2n+1(partial derivative u/partial derivative z) = (partial derivative u/partial derivative z)(2n+1) / (partial derivative u/partial derivative z)(2) (2n+1)/2 and N2n+1 (partial derivative u/partial derivative y) = (partial derivative u/partial derivative y)(2n+1) /(partial derivative u/partial derivative y)(2) (2n+1)/2 which should be zero if local isotropy is satisfied (n is a positive integer). It is found that the relation M2n+1(partial derivative u/partial derivative z) similar to R-lambda(-1) is supported reasonably well by hot- wire data up to the direction of the mean shear; its effect on M2n+1(partial derivative u/partial derivative z) (in the non- shear direction) is negligible. seventh order (n = 3) on the wake centreline, although it is also dependent on the initial conditions. The present relation N3(partial derivative u/partial derivative y) similar to R-1 is obtained more rigorously than that proposed by Lumley (Phys Fluids 10: 855-858, 1967) via dimensional arguments. The effect of the mean shear at locations away from the wake centreline on M2n+ 1(partial derivative u/partial derivative z) and N2n+ 1(partial derivative u/partial derivative y) is addressed and reveals that, although the non- dimensional shear parameter is much smaller in wakes than in a homogeneous shear flow, it has a significant effect on the evolution of N2n+1(partial derivative u/partial derivative y) in the