Full text loading...
Mean velocity distributions. The thin red line in panel (a) denotes the standard law of the wall, compounding u + = y + with u + = y +/k + C, k = 0.394, C = 4.84. The circles indicate experimental data by Smith 22 at . Panel (b) shows the diagnostic function Ξ (as defined in Eq. (1) ), the horizontal line denoting the reference 1/k log-law value. See Table I for line legend.
Distribution of transformed skin friction (C f i, as defined in Eq. (2) ), and peak streamwise velocity variance. Circles denote data from the TBL1-4 DNS datasets. Incompressible DNS data are shown from Schlatter and Örlü 13 (squares), Simens et al. 14 (diamonds), and Sillero et al. 15 (triangles). Low-speed experimental data from Smith 22 are shown with gradient symbols. In panel (a), the dashed line indicates Eq. (3) , and the solid line Eq. (4) . In panel (b), the solid line indicates Eq. (5) , and the dashed line Eq. (6) .
Instantaneous streamwise velocity field in x − z plane at y + = 15 for TBL4 dataset. Contour levels are shown for −0.25 ⩽ u ′/u ∞ ⩽ 0.25, from dark to light shades. The figure inset shows a zoom of a small rectangular region, to highlight the turbulence fine scales.
Pre-multiplied spanwise spectral densities of u ′ in inner scaling. In panel (a) data are shown at y + = 15 for TBL1-4 (see Table I for line legend). In panel (b) spectra are shown for TBL4 at y + = 15 (solid), 44 (dashes), 70 (dash-dots), 97 (dots), 125 (long dashes), 156 (dash-dot-dot). The horizontal line in (a) is indicative of behavior.
Compensated spanwise spectral densities of u ′ in outer scaling. In panel (a) data are shown at y/δ = 0.3 or TBL1-4 (see Table I for line legend). In panel (b) spectra are shown for TBL4 at y/δ = 0.15 (dots), 0.2 (dashes), 0.3 (solid), 0.5 (dash-dots), 0.7 (long dashes), and 0.9 (dash-dot-dot). The horizontal line in (a) is indicative of behavior.
Summary of parameters for DNS study. L x and L z are the streamwise and spanwise domain lengths, respectively. is the “incompressible” momentum thickness Reynolds number, defined in Eq. (2) . Grid spacings are given in wall units taken at for TBL1, for TBL2, for TBL3, and for TBL4.
Article metrics loading...