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

Towards local isotropy of higher-order statistics in the intermediate wake 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, $${M_{2n + 1}}(\partial u/\partial z) = {{\overline{{{(\partial u/\partial z)}^{2n + 1}}} }}/{{{{\overline{{{(\partial u/\partial z)}^2}} }^{(2n + 1)/2}}}}$$ M 2 n + 1 ( ∂ u / ∂ z ) = ( ∂ u / ∂ z ) 2 n + 1 ¯ / ( ∂ u / ∂ z ) 2 ¯ ( 2 n + 1 ) / 2 and $${N_{2n + 1}}(\partial u/\partial y) = {{\overline{{{(\partial u/\partial y)}^{2n + 1}}} }}/{{{{\overline{{{(\partial u/\partial y)}^2}} }^{(2n + 1)/2}}}}$$ N 2 n + 1 ( ∂ u / ∂ y ) = ( ∂ u / ∂ y ) 2 n + 1 ¯ / ( ∂ u / ∂ y ) 2 ¯ ( 2 n + 1 ) / 2 , which should be zero if local isotropy is satisfied (n is a positive integer). It is found that the relation $$M_{2n+1}(\partial u/\partial z) \sim R_\lambda ^{-1}$$ M 2 n + 1 ( ∂ u / ∂ z ) ∼ R λ - 1 is supported reasonably well by hot-wire data up to the seventh order ( $$n=3$$ n = 3 ) on the wake centreline, although it is also dependent on the initial conditions. The present relation $$N_{3}(\partial u/\partial y) \sim R_\lambda ^{-1}$$ N 3 ( ∂ u / ∂ y ) ∼ R λ - 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 $$M_{2n+1}(\partial u/\partial z)$$ M 2 n + 1 ( ∂ u / ∂ z ) and $$N_{2n+1}(\partial u/\partial y)$$ N 2 n + 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 $$N_{2n+1}(\partial u/\partial y)$$ N 2 n + 1 ( ∂ u / ∂ y ) in the direction of the mean shear; its effect on $$M_{2n+1}(\partial u/\partial z)$$ M 2 n + 1 ( ∂ u / ∂ z ) (in the non-shear direction) is negligible. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Experiments in Fluids Springer Journals

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

, Volume 57 (7) – Jun 14, 2016
8 pages

/lp/springer_journal/towards-local-isotropy-of-higher-order-statistics-in-the-intermediate-CMm8PBhbYp
Publisher
Springer Berlin Heidelberg
Copyright © 2016 by Springer-Verlag Berlin Heidelberg
Subject
Engineering; Engineering Fluid Dynamics; Fluid- and Aerodynamics; Engineering Thermodynamics, Heat and Mass Transfer
ISSN
0723-4864
eISSN
1432-1114
D.O.I.
10.1007/s00348-016-2198-5
Publisher site
See Article on Publisher Site

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month ### Explore the DeepDyve Library ### Unlimited reading Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere. ### Stay up to date Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates. ### Organize your research It’s easy to organize your research with our built-in tools. ### Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. ### Monthly Plan • Read unlimited articles • Personalized recommendations • No expiration • Print 20 pages per month • 20% off on PDF purchases • Organize your research • Get updates on your journals and topic searches$49/month

14-day Free Trial

Best Deal — 39% off

### Annual Plan

• All the features of the Professional Plan, but for 39% off!
• Billed annually
• No expiration
• For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.

$588$360/year

billed annually

14-day Free Trial