(a) Isolines of in the plane. (b) Isolines of in the plane. Solid isolines are from Re590 and dashed isolines are from Re934. Numbers on the isolines indicate the value of that specific isoline. The heavy solid line is κy +.
(a) Scale energy balance at y + = 10 (viscous sublayer/buffer region). (b) Individual contributions of terms from (a). −Π e is the effective production; −T r is the transfer in scale space; E e is the effective dissipation; filled symbols represent (Π e + T r ). Dashed lines and filled circles are from Re934; solid lines and filled squares are from Re590; dashed-dotted-dotted lines and filled diamonds are from Re300; dashed-dotted lines and filled triangles are from Re180. −Π is the turbulent production; −T c is the transfer in physical space; E is the turbulent dissipation; D r and D c are the diffusion in r-space and physical space, respectively.
(a) Scale energy balance at y + = 100 (inner logarithmic region). (b) Individual contributions of terms from (a). Definitions of the various terms are the same as in Figure 2. The vertical dashed line in (a) represents the cross-over scale at Re τ = 934.
(a) Scale energy balance at y + = 250 (outer logarithmic region). (b) Scale energy balance at y/δ = 0.8 (outer region). Definitions of the various terms are the same as in Figure 2. Dashed lines and filled circles are from Re934; solid lines and filled squares are from Re590.
(a) Contour plot of T r (r +,y +) (b) Contour plot of T c (r +,y +). In both plots, the zero contour line is shown by the dashed-dotted line. Positive contours are shown with solid lines and negative contours are shown with dashed lines. The data shown in these plots are from Re590.
(a) Variation of cross-over scale with y + for all DNS datasets. (b) Variation of shear scale and with y + for Reynolds numbers in the range Re τ = 300–2000. The straight line is the asymptotic prediction in the logarithmic layer κy +. The symbols represent from the four Reynolds numbers rescaled by the same constant of order one chosen to match the shear scale for the largest available Reynolds number Re934.
Parameters of the DNS datasets. Details of the datasets are available in Re180;2 Re300;13 Re590;8 Re934.14 The wall-normal spacings Δy + indicated are at the center of the channel.
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