This study utilized direct numerical simulation to investigate the bypass transition over a flat plate featuring isotropic, protruding rough surface and subjected to a favorable-to-adverse pressure gradient. The rough surface was positioned at one of two locations, upstream of or in proximity to the separation point, while the inlet free-stream turbulence (FST) was characterized by two distinct intensities and fundamental frequencies. Through proper orthogonal decomposition, dynamic mode decomposition, local stability, and transient growth analyses, the effects of rough surfaces and inlet FST with varying intensities and fundamental frequencies on the bypass transition process and its disturbance growth mechanism were elucidated. The results indicate that the intensity and fundamental frequency of the inlet FST, along with the rough surface position, have negligible effects on the quasistreamwise vortices and velocity streak structures in the transition region. The rough surface placed upstream of the separation point interacts with the inlet FST to generate a resonant mode. For an inlet FST with a turbulence intensity of 3% and a fundamental frequency of $2\pi /7$, this interaction produces a novel resonant mode distinguished by a more elongated wave packet and an upstream-shifted resonant onset. This new mode comprises numerous high-frequency components that make a significant collective contribution to the system's nonlinear dynamics. Conversely, a rough surface positioned near the separation point markedly amplifies the inlet FST. The second harmonic of the inlet FST demonstrates insensitivity to the rough surface's position, the FST intensity, and its fundamental frequency. A lower fundamental frequency of the inlet FST results in increased nonlinear structural strength within its third and fourth harmonics, an effect that is further augmented when the rough surface is located near the separation point. The novel resonant mode creates extensive regions of linear stability within the transition zone. Within these regions, disturbances at multiple frequencies undergo optimal transient growth, and the spatial distribution of these optimal disturbances mirrors the fibrous morphology of the corresponding energy structure. Regarding the transient growth of wave disturbances in general resonant modes, a higher fundamental frequency yields the maximum energy gain, albeit within the most spatially confined optimal disturbance distribution. Furthermore, an increase in the streamwise wave number of the travelling wave also serves to enhance the gain.

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• Flow instability
• Transition to turbulence