Self-sustaining process of minimal attached eddies in turbulent channel flow
File(s)
Accepted version
Author(s)
Hwang, Y
Bengana, Y
Type
Journal Article
Abstract
It has been recently shown that the energy-containing motions (i.e. coherent structures) in turbulent channel flow exist in the form of Townsend’s attached eddies by a numerical experiment which simulates the energy-containing motions only at a prescribed spanwise length scale using their self-sustaining nature (Hwang, J. Fluid Mech., vol. 767, 2015, pp. 254–289). In the present study, a detailed investigation of the self-sustaining process of the energy-containing motions at each spanwise length scale (i.e. the attached eddies) in the logarithmic and outer regions is carried out with an emphasis on its relevance to ‘bursting’, which refers to an energetic temporal oscillation of the motions (Flores & Jiménez, Phys. Fluids, vol. 22, 2010, 071704). It is shown that the attached eddies in the logarithmic and outer regions, composed of streaks and quasi-streamwise vortical structures, bear the self-sustaining process remarkably similar to that in the near-wall region: i.e. the streaks are significantly amplified by the quasi-streamwise vortices via the lift-up effect; the amplified streaks subsequently undergo a ‘rapid streamwise meandering motion’, reminiscent of streak instability or transient growth, which eventually results in breakdown of the streaks and regeneration of new quasi-streamwise vortices. For the attached eddies at a given spanwise length scale λz between λ+z≃100 and λz≃1.5h , the single turnover time period of the self-sustaining process is found to be Tuτ/λz≃2 ( uτ is the friction velocity), which corresponds well to the time scale of the bursting. Two additional numerical experiments, designed to artificially suppress the lift-up effect and the streak meandering motions, respectively, reveal that these processes are essential ingredients of the self-sustaining process of the attached eddies in the logarithmic and outer regions, consistent with several previous theoretical studies. It is also shown that the artificial suppression of the lift-up effect of the attached eddies in the logarithmic and outer regions leads to substantial amounts of turbulent skin-friction reduction.
Date Issued
2016-05-25
Date Acceptance
2016-03-28
Citation
Journal of Fluid Mechanics, 2016, 795, pp.708-738
ISSN
1469-7645
Publisher
Cambridge University Press (CUP)
Start Page
708
End Page
738
Journal / Book Title
Journal of Fluid Mechanics
Volume
795
Copyright Statement
The final publication is available via Cambridge Journals Online at http://dx.doi.org/10.1017/jfm.2016.226
Sponsor
Engineering and Physical Sciences Research Council
Engineering & Physical Science Research Council (EPSRC)
Grant Number
EP/N019342/1
EP/N019342/1
Subjects
Fluids & Plasmas
01 Mathematical Sciences
09 Engineering
Publication Status
Published
Date Publish Online
2016-04-20