Effects of ripples on turbulence structure and drag forces on wavy walls

Turbulence structure and friction and pressure forces acting on two-dimensional wavy walls with and without ripples are numerically investigated. A three-dimensional direct numerical simulation (DNS) based on a finite difference method is applied to turbulent boundary layer over the wavy walls. Two conventional methods for estimating the friction velocity from the log-law of the mean velocity and the Reynolds stress in the vicinity of the wall were also examined by applying the results of the DNS. The results show that the turbulence intensities, turbulence kinetic energy and Reynolds stress over the wavy wall with ripples are larger than those over the wavy wall without ripples. The ratios of the friction drag to the total drag are 0.47 and 0.32 for the wavy walls with and without ripples, respectively. Both conventional methods overestimate the friction velocity at 49% and 25% for the wavy wall without ripples and at 69% and 50% for the wavy wall with ripples. The predictions suggest that friction velocity on the wind-driven wavy air-water interface does not increase linearly with free-stream wind-speed as reported in the previous studies because of the generation of ripples on the wavy interface.