Towards local isotropy of higher-order statistics in the intermediate wake

© 2016, Springer-Verlag Berlin Heidelberg.
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(?u/?z)=(?u/?z)2n+1¯/(?u/?z)2¯(2n+1)/2 and N2n+1(?u/?y)=(?u/?y)2n+1¯/(?u/?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(?u/?z)~R?-1 is supported reasonably well by hot-wire data up to the seventh order (n = 3) on the wake centreline, although it is also dependent on the initial conditions. The present relation N3(?u/?y)~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(?u/?z) and N2n+1(?u/?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(?u/?y) in the direction of the mean shear; its effect on M2n+1(?u/?z) (in the non-shear direction) is negligible.