Turbulent boundary layer experiments above a smooth wall and two-dimensional (2D) rod-roughened walls are conducted to investigate the effects of friction Reynolds numbers ${\text{Re}}_{\tau }$ and streamwise spacing of the roughness elements on the flow properties. The first study uses the roughness pitch $p$ to height $k$ ratio $p/k=8$ and a range of friction Reynolds numbers, $1840\le {\mathrm{Re}}_{\tau }\le 7500$. The result shows that the drag coefficient $C_f$ converges to the fully rough condition (akin to the classic k-type roughness at a fully developed state) with large roughness Reynolds numbers ($k^{+}>75$) when the friction Reynolds number reaches ${\mathrm{Re}}_{\tau }\ge 3900$ and the relative roughness height is $k/{\delta }_{99}\ge 0.02$, where ${\delta }_{99}$ is the boundary layer thickness. As ${\mathrm{Re}}_{\tau }$ increases, the premultiplied energy spectra show that the normalized energy of the near-wall cycle decreases, while the large-scale structures become more dominant. The second study uses a wide range of $p/k$ ($2\le p/k\le 128$) at ${\mathrm{Re}}_{\tau }\approx 3500$. The $C_f$ and the roughness function $\mathrm{\Delta }{U}^{+}$ results indicate that the increase of streamwise spacing of the roughness elements $p/k$ induces higher $C_f$ and $\mathrm{\Delta }{U}^{+}$, and it reaches the maximum value at $p/k=8$. For $p/k>8$, the $C_f$ and $\mathrm{\Delta }{U}^{+}$ values decrease as $p/k$ increases, indicating a less severe drag increase. The premultiplied energy spectra also show that the highly energetic near-wall cycle of streaks and quasistreamwise vortices decreases as $p/k$ increases (for all cases from $p/k=2$–128), and they seem to be transported farther from the wall. The trend is slightly different for the largest-scale structures located around the log region. The result suggests that 2D square-bar roughness can reduce the energy distribution for the largest-scale structure for $p/k=2–128$.

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• Boundary layers
• Flow-structure interactions
• Interactions in fluids
• Roughness
• Structure & turbulence of boundary layers
• Turbulence
• Hot-wire anemometry