Direct numerical simulation and modal analyses on transition flow with streamwise adjacent roughness elements

Direct numerical simulation has been employed to investigate the transition in a flat plate boundary layer induced by streamwise adjacent roughness elements, with cylinder or ramp serving as the front roughness element. This study elucidates the impacts on time-averaged and fluctuating velocity fields, vortex structures, and energetic structures, revealing the interplay between the leading modes and the sweep and ejection events. Findings indicate that the ramp's ability to excite fluctuating kinetic energy exceeds that of adjacent cylinders. Moreover, the strong correlation between fluctuating kinetic energy and vorticity gradient is tied to the dissipation term of fluctuating kinetic energy and the production term of enstrophy. The robust vortex pair generated by the ramp, along with its lift-up effect, and the substantial mainstream dilution due to increased streamwise spacing augment the time-averaged velocity gradient and the fluctuating kinetic energy downstream of the back roughness element. Such an enhancement further differentiates the sweep and ejection events corresponding to the cylinder. However, these distinct events corresponding to the ramp remain inseparable. The inherent characteristics of the varicose mode remain invariant with respect to streamwise spacing and the morphology of the front roughness element. The energetic wavepacket induced by the ramp disturbance is closely associated with the time-averaged velocity gradient. The correlation coefficients between the extracted leading mode's sweep and ejection events and the actual physical field's two events range from 0.3 to 0.4, suggesting that the Reynolds shear stress −u′v′¯ induced by streamwise adjacent roughness elements embodies low-rank linear unstable dynamics.