Drag enhancement by the addition of weak and strong waves to a wave-current boundary layer over bumpy walls

We present a comparison of direct numerical simulation results of two wave-current boundary layers over bumpy walls: one in the current-dominated flow regime (wave-driven to steady current ratio of 0.34) and the other in the wave-dominated flow regime (wave-driven to steady current ratio of 1.25), giving respective wave Reynolds numbers of 351 and 4780. The turbulent, wave-current channel flow has a friction Reynolds number of 350 for both cases. At the lower boundary, a bumpy wall is introduced with a direct forcing immersed boundary method, while the top wall has a free-slip boundary condition. For the current-dominated case, despite the hydraulically smooth nature of the wave-driven flow, the addition of waves to the steady flow enhances the turbulent kinetic energy (TKE) dissipation and results in an increase in the relative roughness of 1.4 times the physical roughness and an increase in the drag coefficient by 10%. For the wave-dominated case, the relative roughness increases by a factor of 8 times the physical roughness and the drag coefficient increases by 72%. These results agree with the theoretical predictions by Grant and Madsen (1979), even in the current-dominated regime which should not apply to the theoretical predictions. By analyzing the TKE and Reynolds Stress budgets, we observe that pressure-strain rate correlations for the bumpy wall cases play a significant role in redistributing TKE from the streamwise directions to the other two coordinate directions. Additionally, we observe enhanced second quadrant events responsible for streak lifting or breakdown events resulting in larger dissipation.