Hydrodynamics of the two- and three-dimensional self-propelled swimmer: Effect of degrees of freedom

Self-propelled models are widely used to study fish-like swimming, yet most existing studies rely on two-dimensional simplifications and restricted degrees of freedom in the self-propelled motion. In this study, we systematically investigate how dimensionality and kinematic freedom influence the hydrodynamic performance of self-propelled swimmers by varying the undulation frequency, tailbeat amplitude, and fluid viscosity. The results show that two-dimensional models overestimate swimming speed, while increasing the rotational degrees of freedom reduces the swimming speed in both two- and three-dimensional cases. Generally, higher swimming speeds are consistently associated with higher power expenditure. Based on these results, we identify a data-driven parameter that can map two-dimensional results to their three-dimensional counterparts and clarify the limitations of such simplifications. These findings provide insight into the hydrodynamic performance of swimming fish and offer potential guidance for improving reduced-order models of fish-like locomotion.