Disturbance penetration in Poiseuille flow over sinusoidal and triangular wavy walls

Disturbance penetration in pressure-driven channel flow over corrugated walls has been studied extensively for smooth sinusoidal geometries, whereas corresponding analyses for piecewise-linear triangular profiles remain limited. In the present study, linear perturbation analysis and finite-volume simulations are used to examine the wall-normal disturbance structure and to quantify the penetration depth Pv under identical amplitude and wavelength conditions. For sinusoidal walls, the perturbation results agree well with earlier theoretical and experimental studies, as well as with the present finite-volume simulations. The results show that disturbance penetration is governed by both the viscous length scale θ and the geometric parameter α. Under otherwise identical conditions, triangular walls generally produce weaker penetration than sinusoidal walls, with the difference becoming more pronounced in deeper channels. Over the parameter range considered here, the penetration-depth data follow an approximate relation of the form Pv∼C θ1/3 within selected intermediate ranges of θ. This behavior is most evident for deep-channel configurations, while the prefactor C depends on wall shape and channel confinement.