Quantitative hydrodynamic investigation of fish caudal fin cupping motion using a bio-robotic model

The three-dimensional deformation of fish caudal fin during swimming was reported in several teleost bony fish species, e.g., bluegill sunfish (Lepomis macrochirus) and cichlid fish (Pseudotropheus greshakei). However, few study has addressed the effect of 3D locomotion on its thrust efficiency quantitatively. In this paper, we first performed biological observations on yellow perch (Perca flavescens) and confirmed the evidence of "cupping" motion for the steady swimming behaviors. The biological kinematics data was then extracted and appropriately programmed into to a robotic caudal fin model coupled with heave and pitch oscillatory motions. We then conducted systematic hydrodynamic experiments on this physical model by manipulating Strouhal numbers (St=0.16-0.50). Comparison between the cupping fin motion and the flat motion showed that the thrust force increased by 78% at the St of 0.32, and thrust efficiency increased 16% at the St of 0.28. DPIV experiments in the horizontal plane were conducted at representative experimental scenarios (St=0.22 and 0.5). We found that the cupping motion has a significant effect on the wake structure, which was distinct with the typically found wake structure, for example, reversed Karman vortex reported by many two-dimensional flapping foil studies. Quantitative analysis of wake flow further demonstrated that the caudal fin generated stronger vortex circulation with addition of cupping motion. We hypothesize that the fish may control the cupping motion to obtain better swimming efficiency under different swimming states.