Spectral analysis of turbulence energy transport in a channel mounted with circular-arc ribs

Spectral analysis of the transport process of turbulence kinetic energy (TKE) in a channel roughened with spanwise-aligned circular-arc ribs is conducted based on direct numerical simulations (DNS). Test cases of varying pitch-to-height ratios ( $P/H=3.0$ , 5.0 and 7.5) and bulk Reynolds numbers ( ${\textit{Re}}_b=5600$ and 14 600) are compared. It is observed that the characteristic spanwise wavelength of the energy-containing eddies in the internal shear layer (ISL) increases as the value of $P/H$ increases, but decreases as the Reynolds number increases. In the ISL, the energy transport processes are dominated by turbulent production as the lead source term, but by turbulent diffusion and dissipation as the lead sink terms. It is found that regions with high production and dissipation rates of TKE in the ISL are associated with moderate and small wavelengths, respectively. The TKE production for sustaining moderate- and large-scale motions enhances gradually with an increasing value of $P/H$ , while that for sustaining small-scale motions augments as the Reynolds number increases. It is interesting to observe that the interscale-transport term plays a critical role in draining TKE at moderate wavelengths as a sink and carries the drained TKE to small-scale eddies as a source. It is discovered that a higher pitch-to-height ratio leads to shortening of the characteristic spanwise wavelength of the dissipation process but prolongation of those of the production, interscale-transport and turbulent-diffusion processes in the ISL. By contrast, a higher Reynolds number results in reductions in the characteristic spanwise wavelengths of all spectral transport terms.