Examples of (a) an individual turbulent spot at Re θ ≈ 300, (b) merged turbulent spots at Re θ ≈ 500, and (c) developed turbulence at Re θ = 1840 in the boundary layer near the wall marked by isosurfaces of enstrophy. The dashed lines (yellow online) demarcate the parts of the flow from which data was used to calculate the statistics.
Coefficient of friction as a function of Re θ. Solid line, Wu and Moin27; long-short dashed line, 1/7th power law approximation30; filled circle (red online), conditionally averaged from individual turbulent spots at Re θ ≈ 300 ; filled circle (blue online), conditionally averaged from merged turbulent spots at Re θ ≈ 500.
Mean streamwise velocity distribution: dashed-dotted line, Blasius profile; short dashed line, U + = 2.41 ln y + + 5 in the logarithmic layer; dotted line, Re θ = 1840; solid line (red online), Re θ ≈ 300; and long dashed line (blue online), Re θ ≈ 500 for turbulent spots; open triangles and open and filled circles, Cantwell and Coles5; x, Coles and Barker31; +, Wygnanski et al.,4 and open diamonds, Johansson et al. 8
Distributions of (top), (second from top), (third from top), and (bottom), with normalization by u τ 2. Solid lines (red online), Re θ ≈ 300; dashed lines (blue online), Re θ ≈ 500; dotted lines, Re θ = 1840; open circles, Spalart22 at Re θ = 1410, filled squares, Karlsson and Johansson32 at Re θ = 2420. Open diamonds, data from Johansson et al. 8 sampled in turbulent spots for .
Distributions of the turbulent kinetic energy production and dissipation rates. Solid lines (red online), Re θ ≈ 300; dashed lines (blue online), Re θ ≈ 500; dotted lines, Re θ = 1840; open circles, Spalart22 at Re θ = 1410; and filled squares, Johansson and Karlsson33 at Re θ = 2420.
Distributions of the dissipation rate and enstrophy. For y + > 8, upper curves are enstrophy; lower curves are dissipation rate for each Reynolds number. Solid lines (red online), Re θ ≈ 300; dashed lines (blue online), Re θ ≈ 500; dotted lines Re θ = 1840. Symbols from Spalart22 at Re θ = 1410: filled squares, enstrophy; open circles, dissipation rate.
Distributions of the vorticity component variances. Solid lines (red online), Re θ ≈ 300; dashed lines (blue online), Re θ ≈ 500; dotted lines, Re θ = 1840. Open symbols from Spalart22 at Re θ = 1410, and filled symbols from Ong and Wallace34 at Re θ = 1070.
Particle motions in the wall normal direction illustrating momentum and heat fluxes corresponding to mean gradient transport. Table classifies velocity component and temperature fluctuations in octants according to their sign.
Fractional contributions to momentum and heat fluxes from the eight octants defined in Fig. 8. Numbers and the subscript i in this figure denote these octants. (a)–(c) ⟨uv⟩ i /⟨uv⟩, (d)–(f) ⟨uθ⟩ i /⟨uθ⟩, and (g)–(i) ⟨vθ⟩ i /⟨vθ⟩. From left to right Re θ = 1840, 500, and 300.
Streamline projections on cross-stream (y − z) planes with color coded contours of (a) uv momentum, (b) vθ heat flux in the transitional flow near Re θ = 500, and (c) and (d) in the developed flow near Re θ = 1840.
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