Turbulent momentum and kinetic energy transfer of channel flow over three-dimensional wavy walls

In this paper, we conduct a numerical investigation to analyze the turbulent flow characteristics over three-dimensional wavy walls with varying amplitudes and wavelengths, with a specific focus on the transfer of momentum and kinetic energy. Detailed three-directional momentum statistics are presented to elucidate the influence of shape parameters on flow behavior. The temporal-spatial averaging at relative height is employed to highlight the impact of the wall on mean, time-averaged, and dispersive momentum flux as well as kinetic energy production. Our findings indicate that the current wall amplifies the effects of spanwise momentum flux, which is determined by the transverse flow around the crest. The dispersive shear stress (DSS) demonstrates a notable correlation with vorticity enhancement, while the near-wall vertical momentum flux is jointly governed by the counteraction of Reynolds shear stress and DSS. Through an analysis of kinetic energy conservation, we observe the transfer of kinetic energy among time-averaged, mean, dispersive, and turbulent motions. Overall, kinetic energy is transferred from dispersion to the mean flow and subsequently to turbulence downstream of the crest. On the windward side, both turbulent and dispersive energy are injected into the mean flow, suggesting the possible growth of internal boundary layer. Additionally, the exchange between dispersion and turbulence significantly contributes to turbulent kinetic energy production, particularly in cases with high amplitudes or spanwise wavelengths.