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On coherent structure in wall turbulence

Sharma, A. S. and McKeon, B. J. (2013) On coherent structure in wall turbulence. Journal of Fluid Mechanics, 728 . pp. 196-238. ISSN 0022-1120. https://resolver.caltech.edu/CaltechAUTHORS:20130820-101633052

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Abstract

A new theory of coherent structure in wall turbulence is presented. The theory is the first to predict packets of hairpin vortices and other structure in turbulence, and their dynamics, based on an analysis of the Navier–Stokes equations, under an assumption of a turbulent mean profile. The assumption of the turbulent mean acts as a restriction on the class of possible structures. It is shown that the coherent structure is a manifestation of essentially low-dimensional flow dynamics, arising from a critical-layer mechanism. Using the decomposition presented in McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382), complex coherent structure is recreated from minimal superpositions of response modes predicted by the analysis, which take the form of radially varying travelling waves. The leading modes effectively constitute a low-dimensional description of the turbulent flow, which is optimal in the sense of describing the resonant effects around the critical layer and which minimally predicts all types of structure. The approach is general for the full range of scales. By way of example, simple combinations of these modes are offered that predict hairpins and modulated hairpin packets. The example combinations are chosen to represent observed structure, consistent with the nonlinear triadic interaction for wavenumbers that is required for self-interaction of structures. The combination of the three leading response modes at streamwise wavenumbers 6; 1; 7 and spanwise wavenumbers ±6; ±6; ±12, respectively, with phase velocity 2/3, is understood to represent a turbulence ‘kernel’, which, it is proposed, constitutes a self-exciting process analogous to the near-wall cycle. Together, these interactions explain how the mode combinations may self-organize and self-sustain to produce experimentally observed structure. The phase interaction also leads to insight into skewness and correlation results known in the literature. It is also shown that the very large-scale motions act to organize hairpin-like structures such that they co-locate with areas of low streamwise momentum, by a mechanism of locally altering the shear profile. These energetic streamwise structures arise naturally from the resolvent analysis, rather than by a summation of hairpin packets. In addition, these packets are modulated through a ‘beat’ effect. The relationship between Taylor’s hypothesis and coherence is discussed, and both are shown to be the consequence of the localization of the response modes around the critical layer. A pleasing link is made to the classical laminar inviscid theory, whereby the essential mechanism underlying the hairpin vortex is captured by two obliquely interacting Kelvin–Stuart (cat’s eye) vortices. Evidence for the theory is presented based on comparison with observations of structure in turbulent flow reported in the experimental and numerical simulation literature and with exact solutions reported in the transitional literature.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1017/jfm.2013.286 DOIArticle
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=8952239PublisherArticle
http://arxiv.org/abs/1301.7580arXivDiscussion Paper
ORCID:
AuthorORCID
Sharma, A. S.0000-0002-7170-1627
McKeon, B. J.0000-0003-4220-1583
Additional Information:© 2013 Cambridge University Press. Received 16 July 2012; revised 23 May 2013; accepted 29 May 2013; first published online 8 July 2013. The support of the Air Force Office of Scientific Research Aerothermodynamics and Turbulence portfolio, under grant no. FA9550-08-1-0049 (Program Manager J. Schmisseur), is gratefully acknowledged by B.J.M. A substantial portion of this work was completed while A.S. was with the Department of Automatic Control and Systems Engineering at the University of Sheffield, UK.
Group:GALCIT
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Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)FA9550-08-1-0049
Subject Keywords:low-dimensional models; turbulence theory; turbulent boundary layers
Record Number:CaltechAUTHORS:20130820-101633052
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20130820-101633052
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:40732
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:20 Aug 2013 22:13
Last Modified:03 Oct 2019 05:42

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