Abstract
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 (0.5~1.1) and tail-beat frequency (2 Hz~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.
Highlights
After millions of years of evolution, fish have evolved with extremely excellent propulsive capabilities, which are far superior to those of man-made watercrafts
The wavelength is varied with the fish species, and this difference in present study is analysed by the complex orthogonal decomposition (COD) method
The results show that the travelling index increases with the wave number until reaching a stable value, as
Summary
After millions of years of evolution, fish have evolved with extremely excellent propulsive capabilities, which are far superior to those of man-made watercrafts. For example, saithe, mackerel and bass, carangiform fish have a streamlined body with a homocercal caudal fin. As suggested by Videler [2], the fish-like movement is described by the approximate trajectory of midline motion h( x, t), which is identified by a sinusoidal travelling wave with an increasing amplitude envelope. It is expressed as: h( x, t) = a1 + a2 x + a3 x2 sin(ωt − kx )
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