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On coherent structure in wall turbulence

On coherent structure in wall turbulence
On coherent structure in wall turbulence
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, 658, 2010), complex coherent structure is recreated from minimal superpositions of response modes predicted by the analysis, which take the form of radially-varying travelling waves. By way of example, simple combinations of these modes are offered that predicts hairpins and modulated hairpin packets. The phase interaction also predicts important skewness and correlation results known in the literature. It is also shown that the very large scale motions act to organise hairpin-like structures such that they co-locate with areas of low streamwise momentum, by a mechanism of locally varying the shear profile. The relationship between Taylor's hypothesis and coherence is discussed and both are shown to be the consequence of the localisation 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 to observations of structure reported in the experimental, transitional flow and turbulent flow numerical simulation literature.
0022-1120
196-238
Sharma, A.S.
cdd9deae-6f3a-40d9-864c-76baf85d8718
McKeon, B.J.
2e685015-292a-42a7-8c9e-7cc27cf2da67
Sharma, A.S.
cdd9deae-6f3a-40d9-864c-76baf85d8718
McKeon, B.J.
2e685015-292a-42a7-8c9e-7cc27cf2da67

Sharma, A.S. and McKeon, B.J. (2013) On coherent structure in wall turbulence. Journal of Fluid Mechanics, 728, 196-238. (doi:10.1017/jfm.2013.286).

Record type: Article

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, 658, 2010), complex coherent structure is recreated from minimal superpositions of response modes predicted by the analysis, which take the form of radially-varying travelling waves. By way of example, simple combinations of these modes are offered that predicts hairpins and modulated hairpin packets. The phase interaction also predicts important skewness and correlation results known in the literature. It is also shown that the very large scale motions act to organise hairpin-like structures such that they co-locate with areas of low streamwise momentum, by a mechanism of locally varying the shear profile. The relationship between Taylor's hypothesis and coherence is discussed and both are shown to be the consequence of the localisation 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 to observations of structure reported in the experimental, transitional flow and turbulent flow numerical simulation literature.

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More information

Submitted date: 12 July 2012
Published date: 29 May 2013
Organisations: Aerodynamics & Flight Mechanics Group

Identifiers

Local EPrints ID: 350309
URI: http://eprints.soton.ac.uk/id/eprint/350309
ISSN: 0022-1120
PURE UUID: f9f21196-5aa7-46f0-9b07-d4d4a0fb741b
ORCID for A.S. Sharma: ORCID iD orcid.org/0000-0002-7170-1627

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Date deposited: 25 Mar 2013 12:32
Last modified: 26 Nov 2021 03:00

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Contributors

Author: A.S. Sharma ORCID iD
Author: B.J. McKeon

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