Unsteady and Transitional Flows Behind Roughness Elements

The role of surface roughness in boundary layers continues to be a topic of significant interest, especially with regard to how controlled roughness might be used to delay laminar-to-turbulent transition. Although it may be useful for control, large-amplitude roughness may itself lead to transition. In an effort to understand the breakdown mechanics associated with large-amplitude surface roughness, experiments are conducted to investigate the steady and unsteady disturbances generated by three-dimensional roughness elements whose amplitudes are close to the critical roughness-based Reynolds number Re k for roughness-induced transition. Measurements are obtained in a flat-plate boundary layer downstream of a spanwise array of cylindrical roughness elements at both subcritical and supercritical values of Re k . The steady disturbance field has strong shear in the wall-normal and spanwise directions, and the unsteady streamwise velocities in the roughness elements' wake show evidence of hairpin vortices. The locations of maximum fluctuation intensity correspond to the locations of inflection points in the steady flow streamwise velocity, and this suggests that the fluctuations may result from a Kelvin-Helmholtz-type instability. Temporal power spectra indicate an unstable band of frequencies from 300 to 800 Hz. The Strouhal number associated with the 650-Hz fluctuations that are often observed to be the strongest give Sr = 0.15, a value that is in good agreement with previous findings. At supercritical Re k , rapid transition takes place when the unsteady disturbances reach nonlinear amplitudes. The disturbance growth rates indicate that in this situation transition can be understood as a competition between the unsteady disturbance growth and the rapid relaxation of the steady flow that tends to stabilize these disturbances.