Relationship between wall shear stresses and streamwise vortices in turbulent flows over wavy boundaries

The relationship between wall shear stresses and near-wall streamwise vortices is investigated via a direct numerical simulation(DNS) of turbulent flows over a wavy boundary with traveling-wave motion. The results indicate that the wall shear stresses are still closely related to the near-wall streamwise vortices in the presence of a wave. The wave age and wave phase significantly affect the distribution of a two-point correlation coefficient between the wall shear stresses and streamwise vorticity. For the slow wave case of c/Um = 0.14, the correlation is attenuated above the leeward side while the distribution of correlation function is more elongated and also exhibits a larger vertical extent above the crest. With respect to the fast wave case of c/U_m=1.4, the distribution of the correlation function is recovered in a manner similar to that in the flat-wall case. In this case, the maximum correlation coefficient exhibits only slight differences at different wave phases while the vertical distribution of the correlation function depends on the wave phase.