Hydrodynamics and scaling laws for the two-degree-of-freedom propulsion of an undulating swimmer

The fluid mechanism underlying the remarkable swimming capabilities of fish remains incompletely understood. In this paper, fish swimming is simplified as the two-degree-of-freedom self-propulsion of an undulating swimmer, and the combined effects of frequency and wavelength on its performance are numerically studied. It is found that the optimal wavelength is approximately λ = 1.25, at which the maximum cruising speed is achieved. Moreover, some simple scaling laws with respect to frequency and wavelength are established to predict the propulsive performance of the undulating swimmer. On the other hand, the hydrodynamic mechanism underlying thrust generation of the undulating swimmer is analyzed in detail. It is shown that the net thrust is primarily generated by its posterior body, and its head contributes positively only when the wavelength is large enough. The findings may contribute to a deeper understanding of fish swimming and the optimization of bio-inspired underwater robots.