Forced motion modes of a patch of flexible rods in open channel flows

Flexible vegetation is common in riverine and coastal ecosystems. The patch of flexible vegetation is influenced by various factors, resulting in a series of characteristic modes of motion. This study aims to investigate the influence of the Cauchy number (Ca, the ratio of the hydrodynamic drag force to the bending rigidity, i.e., the inverse of the dimensionless bending rigidity) and the solid volume fraction (which reflects the distribution density of a patch of flexible rods) on the motion modes. Additionally, the induction mechanism of fluid and flexible vegetation interaction on motion modes is investigated. A semi-resolved coupling numerical model was employed to simulate the fluid and structure interaction. The results show that the Cauchy number and solid volume fraction influence the motion modes to different extents. Notably, the effect of Ca was significant within the designed range of the two parameters. The wavelength of the monami mode generally shows little variation compared to that observed in the Kelvin–Helmholtz (K-H) vortex, which results from the mixing layer flow instability. The physical mechanism that the motion mode of a patch of flexible rods is induced by the interaction between water flow and flexible rods is further validated and cognized. When the K-H vortex frequency, the natural frequency of the patch in water, and the motion frequency of the patch are close, the patch exhibits motion in the monami mode. Otherwise, the patch will exhibit motion in erect, swaying, and prone mode.