Disturbance growth analysis of pressure gradient transition flow with three-dimensional rough surfaces

This study employs direct numerical simulations to examine the laminar-to-turbulent transition over a flat plate subjected to a favourable–adverse pressure gradient, incorporating isotropic/anisotropic and negatively skewed rough surfaces. The rough surfaces are positioned upstream of the separation point. By leveraging global stability analysis, inlet/local transient growth analysis and resolvent analysis, the combined effects of rough surface and adverse pressure gradients on disturbance growth mechanisms during transition are elucidated. The findings indicate that isotropic rough surfaces are most likely to trigger global instability, while streamwise modulation demonstrates the strongest inertia in this regard. Convective-type modes dominate near the outlet. As the system approaches the instability threshold, a critical mode emerges in the three-dimensional shear layer downstream of the roughness, characterised by a streamwise velocity peak reminiscent of a laminar separation bubble, with disturbance kinetic energy governed primarily by streamwise shear. The isotropy of the rough surface significantly amplifies linear instability of local travelling waves, transforming the downstream region into both a low-pass filter and an amplifier of high-wavenumber disturbances. Optimal disturbances of local travelling waves in the far downstream exhibit a structure analogous to oblique waves. When harmonic nonlinear forcing is introduced, streamwise modulation emerges as the geometry yielding maximum energy gain. The optimal forcing generated is highly localised in wave packets near the downstream region. Excluding the influence of optimal forcing on the harmonic forcings disrupts the coherence of roughness-induced coherent structures, impeding nonlinear interactions in the downstream region and the overall transition process.