Hydrodynamics of a trapezoidal self-propelled flexible plate.*

A trapezoidal self-propelled flexible plate in a quiescent flow was simulated using an immersed boundary method. The shape ratio (S = W_t/W_l) was defined as the ratio of the trailing edge width (W_t) to the leading edge width (W_l). To reveal the hydrodynamics of the plate, the averaged cruising speed (U_c), the input power (P), and the swimming efficiency (η) were analyzed as a function of the bending rigidity (γ) and the shape ratio (S). The three-dimensional effect on the dynamics of the plate was scrutinized with the kinematics such as the peak-to-peak amplitude (A_t/A) and the Strouhal number (St). The elongated body theory was adopted to see the relation between the kinematics and dynamics. The maximum angle of attack (Φ_max) and the mean effective length (L_eff) were examined to account for the hydrodynamics of the self-propelled flexible plate. The vortical structures around the plate were visualized, and the influence of the tip vortex on the swimming efficiency was explored qualitatively and quantitatively.