Towards Local Isotropy of Higher Order Statistics in Wakes
Résumé
In this paper, we test 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) = \textless((partial derivative u/partial derivative z)(2n+1))over bar\textgreater/\textless((partial derivative u/partial derivative z)(2))over bar\textgreater((2n+ 1)/2) on the wake centreline, 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 seventh-order (n = 3), although it is also dependent on the initial conditions. In particular, the present data show that the higher the order (e.g. fifth-or seventh-order), the higher R-lambda must be for local isotropy to be satisfied (i.e. M2n+1(partial derivative u/partial derivative z) = 0).