Time-frequency analysis for two cases of boundary-layer transition induced by random distributed roughness

The boundary layer transition induced by distributed surface roughness has great practical relevance, but remains poorly understood. In this experimental work, we investigate the transition in a flat-plate boundary layer downstream of a localized strip of random distributed roughness. The boundary layer exhibits different temporal and spectral behaviour in two (roughness-) Reynolds-number regimes separated by a critical value. In the “sub-critical” regime, the velocity signals show presence of “turbulent spots”, whereas in the “super-critical” regime, no distinct turbulent spots are observed. Two boundary-layer profiles, one each from the sub-critical and super-critical regimes, are chosen for comparison. The sub-critical case exhibits a bi-modal power spectrum having two humps in frequency ranges differing by an order of magnitude, whereas the super-critical case has a uni-modal spectrum with a single hump in the high-frequency range. The wavelet analysis shows that the energy distribution is intermittent in time for both the cases at all frequencies. However, for the sub-critical case, the energy in the high-frequency range appears as clusters, which are seen as turbulent spots in the velocity signal. On the other hand, for the super-critical case there is no such clustering, consistent with the absence of spots in the velocity signal. We conjecture that, for the sub-critical case, the motions corresponding to the low-frequency spectral hump (possibly the streamwise streaks) could be responsible for imparting organization to the high-frequency motions in the form of turbulent spots. We also detect “events” in the wavelet-energy time series. For the sub-critical case, the events in the high-frequency range have a higher degree of time-localization, which increases with frequency. For the super-critical case, however, the time-localization is independent of frequency over nearly the entire frequency range. These findings present two different scenarios for the late stages of transition, having distinct time-frequency behaviour. This could have implications towards modelling roughness-induced transition.