Fig. 1. Apteronotus albifrons, the black ghost knifefish of South America. (A) Photograph courtesy of Neil Hepworth, Practical Fishkeeping magazine. Inset shows side view of the fish to illustrate the angle of the fin with respect to the body. (B) Frame of video of the fish swimming in a water tunnel, from ventral side. (C) Model of the ribbon fin, shown together with symbols for fin length (L_fin), fin height (h_fin) and two of the kinematic state variables, angular deflection () and the vector from the rotational axis to a point on the fin (r_m). The Eulerian (fluid) reference frame (x, y, z; positive direction indicated by inset) is shown together with names for velocities in the body frame fixed to the rigid fin rotation axis indicated by the red line (surge, heave, sway, roll, pitch, yaw; positive direction indicated by arrows). In this work, simulations were performed with the body-fixed frame oriented to the Eulerian frame as illustrated, and forces are with respect to a traveling wave moving in the head-to-tail direction indicated.