Numerical simulations are conducted to investigate the near-bed flow behaviors of submarine canyons with periodic ridge-valley topography on continental slopes. In the numerical simulation, two topographic parameters are defined: α represents the basal slope angle of the continental slope, and β denotes the side slope angle of the submarine canyon. The topographic modulation of these two parameters on near-bed flow velocity and pipeline on-bottom stability is explored. The results show that the ribbed slope exerts two distinct modulation mechanisms on near-bed flow fields, which are governed by the relative angle between incoming flow and ridge-valley structures. When the flow is perpendicular to the canyon axis (θ = 0°), local topographic contraction and expansion accelerate flow over ridge crests and reduce near-bed velocity in valleys as β increases. In contrast, when the flow is parallel to the canyon (θ = 90°), lateral confinement by bilateral ridges forms a topographic channel, leading to persistent flow acceleration throughout the entire valley area. Moreover, such directional velocity differences substantially alter the on-bottom stability of pipelines deployed within the canyon. Two pipe-soil interaction models are employed in the stability analysis: the Verley-Lund model for a flat clayey seabed and the Slope-Silt model for a sloping silty seabed. The sensitivity of their predictions to soil undrained shear strength is further evaluated.