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Evolution of Lagrangian coherent structures in a cylinder-wake disturbed flat plate boundary layer

Published online by Cambridge University Press:  03 March 2016

Guo-Sheng He ,
Chong Pan ,
Li-Hao Feng ,
Qi Gao  and
Jin-Jun Wang
Guo-Sheng He
Affiliation:
Ministry of Education Key Laboratory of Fluid Mechanics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
Chong Pan
Affiliation:
Ministry of Education Key Laboratory of Fluid Mechanics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
Li-Hao Feng
Affiliation:
Ministry of Education Key Laboratory of Fluid Mechanics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
Qi Gao
Affiliation:
Ministry of Education Key Laboratory of Fluid Mechanics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
Jin-Jun Wang*
Affiliation:
Ministry of Education Key Laboratory of Fluid Mechanics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
*
†Email address for correspondence: [email protected]
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Abstract

Evolution of Lagrangian coherent structures (LCS) in a flat plate boundary layer transition induced by the wake of a circular cylinder is investigated. Both hydrogen bubble visualization and particle image velocimetry (PIV) techniques are used. It is found that downstream of the cylinder, the disturbance in the boundary layer experiences a fast growth followed by a slow decay in the transition. Lagrangian coherent structures are revealed by qualitative hydrogen bubble visualizations and quantitative finite-time Lyapunov exponents (FTLE) fields derived from the PIV data. The evolution of the LCS is considered from the very beginning of the transition up to when the boundary layer becomes fully developed turbulent flow. The mean convection velocity and average inclination angle of the LCS are first extracted from the FTLE fields. The streamwise length of the low-speed streaks seems to increase, while their spanwise distance decreases in the boundary layer transition. Proper orthogonal decomposition (POD) of the PIV data shows that low-speed streaks associated with the hairpin vortices and hairpin packets are the dominant coherent structures close to the wall in the transitional and turbulent boundary layer. The POD modes also reveal a variety of scales in the turbulent boundary layer. Moreover, it is found that large-scale coherent structures can modulate the amplitude of the small-scale ones.

JFM classification

Boundary Layers: Boundary layer structure Instability: Transition to turbulence Wakes/Jets: Wakes
Type
Papers
Information
Journal of Fluid Mechanics , Volume 792 , 10 April 2016 , pp. 274 - 306
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Copyright
© 2016 Cambridge University Press 

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He et al. supplementary movie

Movie 1 – Figure 4：Hydrogen bubble visualization of secondary vortices at the beginning of transition.

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Video 4.1 MB

He et al. supplementary movie

Movie 1 – Figure 4：Hydrogen bubble visualization of secondary vortices at the beginning of transition.

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Video 17 MB

He et al. supplementary movie

Movie 2 – Figure 5：Hydrogen bubble time line visualization of a hairpin vortex in the middle stage of transition.

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Video 2.3 MB

He et al. supplementary movie

Movie 2 – Figure 5：Hydrogen bubble time line visualization of a hairpin vortex in the middle stage of transition.

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Video 9.7 MB

He et al. supplementary movie

Movie 3 – Figure 6：Hydrogen bubble time line visualization of hairpin vortex packet in the turbulent boundary layer.

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Video 2.1 MB

He et al. supplementary movie

Movie 3 – Figure 6：Hydrogen bubble time line visualization of hairpin vortex packet in the turbulent boundary layer.

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Video 9.1 MB

He et al. supplementary movie

Movie 4 – Figure 7：Secondary vortices induced by the wake vortices at the beginning of transition

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Video 3.4 MB

He et al. supplementary movie

Movie 4 – Figure 7：Secondary vortices induced by the wake vortices at the beginning of transition

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Video 4.9 MB

He et al. supplementary movie

Movie 5 – Figure 8：A hairpin vortex in the middle stage of boundary layer transition.

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Video 4.1 MB

He et al. supplementary movie

Movie 5 – Figure 8：A hairpin vortex in the middle stage of boundary layer transition.

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Video 6.6 MB

He et al. supplementary movie

Movie 6 – Figure 9：A hairpin packet in the turbulent boundary layer.

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Video 4.3 MB

He et al. supplementary movie

Movie 6 – Figure 9：A hairpin packet in the turbulent boundary layer.

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Video 4.9 MB

He et al. supplementary movie

Movie 7 – Figure 10：Another example of hairpin packets in the turbulent boundary layer.

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Video 4 MB

He et al. supplementary movie

Movie 7 – Figure 10：Another example of hairpin packets in the turbulent boundary layer.

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Video 5.3 MB