Document Type


Publication Date




Publication Title

Physical Review E






056316 (10 pages)


Flow over a traveling wavy foil with a passively flapping flat plate has been investigated using a multiblock lattice Boltzmann equation and the immersed boundary method. The foil undergoes prescribed undulations in the lateral direction and the rigid flat plate has passive motion determined by the fluid structure interaction. This simplified model is used to study the effect of the fish caudal fin and its flexibility on the locomotion of swimming animals. The flexibility of the caudal fin is modeled by a torsion spring acting about the pivot at the conjuncture of the wavy foil and the flat plate. The study reveals that the passively oscillating flat plate contributes half of the propulsive force. The flexibility, represented by the nondimensional natural frequency F, plays a very important role in the movement and propulsive force generation of the whole body. When the plate is too flexible, the drag force is observed. As the flat plate becomes more rigid, the propulsive force that is generated when the undulation is confined to last part of the wavy foil becomes larger. The steady movement occurs at F=5. These results are consistent with the observations of some swimming animals in nature. © 2012 American Physical Society.

Original Publication Citation

Liu, N., Peng, Y., Liang, Y., & Lu, X. (2012). Flow over a traveling wavy foil with a passively flapping flat plate. Physical Review E, 85(5), 056316. doi:10.1103/PhysRevE.85.056316