CFD Studies of the Effects of Waveform on Swimming Performance of Carangiform Fish

Carangiform fish, like mackerel, saithe and bass, swim forward by rhythmically passing body waves from the head to the tail. In this paper, the undulating motions are decomposed into the travelling part and the standing part by complex orthogonal decomposition (COD), and the ratio between these two parts, i.e., the travelling index, is proposed to analyse the waveform of fish-like movements. To further study the relative influences of the waveform on swimming performance, a self-propelled model of carangiform fish is developed by the level set/immersed boundary (LS-IB) method, and the in-house code is tested by two cases of flow past a sphere and an oscillating cylinder, respectively. In this study, the travelling index is varied in ranges up to 50% larger or smaller than the biological data. The results show that carangiform fish seem to favour a fast and efficient swimming motion with a travelling index of around 0.6. Meanwhile, we study several numerical cases with different amplitude coefficients (0.5 similar to 1.1) and tail-beat frequency (2 Hz similar to 5 Hz), and then compare their swimming performance with each other. We found that the forward speed is closely related to the travelling index and tail-beat frequency, while the swimming efficiency is increased with the tail-beat frequency and amplitude coefficient. These results are also consistent with biological observations, and they might provide beneficial guidance with respect to the future design of robotic fish.