Coupling effect of streamwise-adjacent roughness elements and inlet free-stream turbulence on the flat-plate transition

To elucidate the influences of varying shapes of adjacent roughness elements and inlet free-stream turbulence (FST) on the transition within a flat boundary layer, particularly the alterations in coherent and energetic structures, linear modes, and their energy-containing components, a direct numerical simulation was conducted on a flat-plate boundary layer with streamwise-adjacent roughness elements and subjected to inlet FST. We designed two distinct front roughness element configurations and four levels of inlet FST. Findings indicate that at higher FST levels, the energy conversion from mean flow to fluctuating flow, prompted by the roughness elements, is suppressed; however, configurations with strong disturbances can counteract the effect of delaying transition through the formation of tight quasi-streamwise vortices. With increasing FST levels, energetic structures within cylinder configuration are transported further downstream, whereas in ramp configuration, energetic wave packets with an extensive streamwise range are produced. At the characteristic low frequency ω=0.32, weak FST with intensity akin to noise elicits a resonator-like mode distribution, which aids in the development of coherent structures yet cannot be used to approximate the same frequency waves within nonlinear systems. At the characteristic high frequency ω=2.3, in light of the inlet FST, the role of linear modes in the nonlinear evolution of the system can be substantially augmented. For the energy-containing segment of linear modes characterized by low-rank dynamics, there is no direct association with the high-frequency modes featuring quasi-orthogonality, and their low-rank attributes do not significantly contribute to the nonlinear progression of the system.