Laminar streaks with spanwise wall forcing

The influence of steady sinusoidal oscillations of spanwise wall velocity on the Klebanoff modes, i.e. unsteady streaky fluctuations induced by free-stream turbulence in the pre-transitional Blasius boundary layer, is investigated numerically. The wall motion induces a spanwise boundary layer which grows downstream as x 1/6 and has an asymptotic analytical solution at large downstream distances. While the forcing has no effect on the initial growth of the streaks, their intensity eventually increases or decreases substantially depending on the relative magnitude between the forcing wavelength and the characteristic length scales of the streaks. The wall actuation enhances the streak intensity if the streak spanwise length scale is much larger than the Blasius boundary layer thickness. The streak energy is instead attenuated when the spanwise viscous diffusion effects play a key role. Wall pressure fluctuations may also be significantly damped in this case. The Klebanoff modes generated by full-spectrum free-stream turbulence are predicted to be attenuated by the wall motion. The asymptotic scaling analysis reveals that there exists an optimal forcing wavelength for full-spectrum streak attenuation as long as the spanwise length scales of the dominant streaks are as large as or smaller than the Blasius boundary layer thickness, a common scenario encountered in experiments. The optimal forcing wavelength is found to be comparable with the streak streamwise length scale. As the amplitude of the wall forcing increases, the reduction of streak intensity grows monotonically. The streaks are completely suppressed in the limit of large amplitude.