## Abstract

© 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.

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.

Original language | English |
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Article number | 111 |

Pages (from-to) | 1-8 |

Journal | Experiments in Fluids |

Volume | 57 |

Issue number | 7 |

Early online date | 14 Jun 2016 |

DOIs | |

Publication status | Published - 1 Jul 2016 |