Evidence of very long meandering features in the logarithmic region of turbulent boundary layers

TLDR: In this article, a publisher's version of an article published in Journal of Fluid Mechanics © 2007 Cambridge University Press, Cambridge, UK. www.cambridge.edu.org/

Abstract: This is a publisher’s version of an article published in Journal of Fluid Mechanics © 2007 Cambridge University Press. www.cambridge.org/

Figures

Figure 3. Streamwise (left) and spanwise (right) two-point correlations of the streamwise velocity fluctuation Ruu calculated at (a, b) zref/δ=0.05; (c, d) zref/δ=0.10; (e, f ) zref/δ=0.15; (g, h) zref/δ=0.50. Symbols show rake data: ( ) Reτ =1120; ( ) Reτ =7610; ( ) Reτ =14 380; ( ) Reτ =19 960. Lines show 45 ◦ inclined plane PIV results (dash-dotted) Reτ =1010; (dashed) Reτ =1840; (solid) Reτ =2800.

Figure 7. Instantaneous flow fields from Reτ =934 channel simulations (del Álamo et al. 2004). Shading shows u fluctuations (a) at z+ =150; (b) at z+ =15 (see upper grey-scale). Plots (c) and (d) show the filtered data at the same respective heights (shading shows negative u fluctuations, grey-scale as figure 4).

Figure 16. Two-dimensional premultiplied energy spectra for various isolated synthetic flow fields. Filled contours show normalized magnitude of kxkyEuu for (a) case I, streamwise-aligned Lx =5δ; (b) case I, streamwise-aligned L=10δ; (c) case I, streamwise-aligned L=20δ; (d) case II, meandering L=20δ. In each case a schematic of the synthetic flow is shown above the spectra (where the grey scale shows streamwise velocity fluctuation).

Figure 10. (i) Contour maps showing variation of one-dimensional pre-multiplied spectra with wall-normal position for (a) Reτ =1010; (b) Reτ =1910; (c) Reτ =2630; (d) Reτ =7300. The y-axis shows length scale in both inner (left) and outer (right) scaling. The x-axis shows wall-normal position for both inner (lower) and outer scaling (upper). The colour scale shows magnitude of kxΦuu/U 2 τ . (+) denote ‘inner’ and ‘outer’ energy sites (white) λ + x =1000, z + =15 and (black) λx =6δ, z=0.06δ. Dot-dashed lines show k −1 x limits λx =15.7z (and z + =100 and λx =0.3δ for plot d). (ii) Corresponding mean profiles of ( ) turbulence intensities and (−) velocity. Dotted line shows u+ = z+. Dashed lines and (+) symbols denote z+ =15 and z=0.06δ. Dot-dashed line shows U+ = (1/κ) ln(z+)+A (where κ =0.41 and A=5.0). Red line shows MK2003 formulation.

Figure 14. Example of signal across the spanwise array of sonic anemometers at SLTEST, z/δ=0.037, Reτ =660 000. The x-axis is reconstructed using Taylor’s hypothesis and a convection velocity based on the local mean, U =5.46m s−1. Shading shows only negative u fluctuations (see grey scale).

Table 1. Experimental parameters for hot-wire rake experiments.