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On the spatial organization of hairpin packets in a turbulent boundary layer at low-to-moderate Reynolds number

Published online by Cambridge University Press:  06 April 2018

Sichao Deng ,
Chong Pan ,
Jinjun Wang Open the ORCID record for Jinjun Wang [Opens in a new window]  and
Guosheng He
Sichao Deng
Affiliation:
Fluid Mechanics Key Laboratory of Ministry of Education, Institute of Fluid Mechanics, Beihang University, Beijing 100191, China
Chong Pan*
Affiliation:
Fluid Mechanics Key Laboratory of Ministry of Education, Institute of Fluid Mechanics, Beihang University, Beijing 100191, China
Jinjun Wang
Affiliation:
Fluid Mechanics Key Laboratory of Ministry of Education, Institute of Fluid Mechanics, Beihang University, Beijing 100191, China
Guosheng He
Affiliation:
Fluid Mechanics Key Laboratory of Ministry of Education, Institute of Fluid Mechanics, Beihang University, Beijing 100191, China
*
†Email address for correspondence: panchong@buaa.edu.cn
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Abstract

The present study is devoted to characterizing the coherent organization of vortical structures, which can be fitted into the paradigm of the hairpin-packet model, in the streamwise–wall-normal plane of a canonical turbulent boundary layer at $Re_{\unicode[STIX]{x1D70F}}=377{-}1093$. Proper orthogonal decomposition (POD) of the planar velocity fields measured via two-dimensional particle image velocimetry, together with a spatio-temporal coherence analysis, shows that the first four leading-order POD modes share both geometric similarity and dynamic coherence and jointly depict the downstream convection of the large-scale Q2/Q4 events, which can be regarded as the low-order imprints of the hairpin packets. A simple low-order indicator is then proposed to extract the inclined interfaces of the hairpin packets, based on which a two-point conditional correlation analysis forms a statistical picture of the spatial organization of multiple prograde vortices aligned along the interface within one packet. A saturation of the self-similar growth of the streamwise gap between two neighbouring vortices is seen. This implies a detachment of the hairpin packets from the inner layer. Both the detachment height and the saturated streamwise spacing are found to scale as $Re_{\unicode[STIX]{x1D70F}}^{1/2}$.

JFM classification

Nonlinear Dynamical Systems: Low-dimensional models Turbulent Flows: Turbulent boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 844 , 10 June 2018 , pp. 635 - 668
Copyright
© 2018 Cambridge University Press 

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Deng et al. supplementary movie

An animation corresponding to Figure 12(a) to depict the time evolution of the large-scale interface revealed in $\bm{V}^L$ at the case of $Re_{ au}=377$.

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