Internal boundary layer development due to impulsive changes in spanwise wall velocity

Abstract

The spatial response of a turbulent boundary layer subjected to a streamwiseperiodic square-wave (SqW) variation of the spanwise wall velocity is investigated experimentally. The SqW forcing is implemented via a setup comprising 48 spanwise-running belts, which is used to assess the influence of the (viscous-scaled) forcing wavelength for: sub-optimal ?⁺_x = 471, near-optimum ?⁺_x = 942, and post-optimal ?⁺_x = 1884 conditions, at a fixed spanwise-velocity amplitude A+ = 12. Previous studies have identified a high phase-wise rate-of-change of the Stokes strain (wall-normal gradient of spanwise velocity) - the Stokes-strain rate (SSR) - to drive the attenuation of turbulence, whereas recovery of turbulence was found when SSR ~ 0 extended over a sufficient fetch of the phase, referred to as subphases I and II, respectively. For the SqW, subphase-I occurs over a fixed short fetch where the sign of wall velocity reverses, whereas subphase-II extends over the rest of the half-phase, where the wall velocity remains constant. These SSRrelated hypotheses are confirmed; the phase-wise variation of turbulence attenuation and recovery, however, is established only for the post-optimal case, owing to its extended fetch of subphase-II. An out-of-phase trend between C_f and the turbulence is elucidated by evaluating the internal boundary layer (IBL) thickness d_i, where C_fand d_ishow a clear correlation.