Identification of lagrangian coherent structures in the turbulent boundary layer |
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Authors: | Chong Pan JinJun Wang and Cao Zhang |
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Institution: | (1) Institute of Fluid Mechanics, Beijing University of Aeronautics and Astronautics, Beijing, 100083, China |
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Abstract: | Using Finite-Time Lyapunov Exponents (FTLE) method, Lagrangian coherent structures (LCSs) in a fully developed flat-plate
turbulent boundary layer are successfully identified from a two-dimensional (2D) velocity field obtained by time-resolved
2D PIV measurement. The typical LCSs in the turbulent boundary layer are hairpin-like structures, which are characterized
as legs of quasi-streamwise vortices extending deep into the near wall region with an inclination angle θ to the wall, and heads of the transverse vortex tube located in the outer region. Statistical analysis on the characteristic
shape of typical LCS reveals that the probability density distribution of θ accords well with t-distribution in the near wall region, but presents a bimodal distribution with two peaks in the outer region, corresponding
to the hairpin head and the hairpin neck, respectively. Spatial correlation analysis of FTLE field is implemented to get the
ensemble-averaged inclination angle θ
R of typical LCS. θ
R first increases and then decreases along the wall-normal direction, similar to that of the mean value of θ. Moreover, the most probable value of θ saturates at y
+=100 with the maximum value of about 24°, suggesting that the most likely position where hairpins transit from the neck to
the head is located around y
+=100. The ensemble- averaged convection velocity U
c of typical LCS is finally calculated from temporal-spatial correlation analysis of FTLE field. It is found that the wall-normal
profile of the convection velocity U
c(y) accords well with the local mean velocity profile U(y) beyond the buffer layer, evidencing that the downstream convection of hairpins determines the transportation properties
of the turbulent boundary layer in the log-region and beyond.
Supported by the National Natural Science Foundation of China (Grant Nos. 10425207 and 10832001) |
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Keywords: | turbulent boundary layer coherent structures vortex identification scheme finite-time Lyapunov exponents hairpin-like |
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