Fluidic undulation effects on carangiform swimmers propelled by internal active bending moments

Abstract

With different shapes and material properties, fish all achieve undulatory swimming gait under the action of internal active muscle stimulation and external fluid forces. Such locomotion can be decomposed into deformation affected by internal and external forces in the body frame and overall translation and rotation solely determined by fluid forces. In order to revisit the undulatory swimming gait, we investigate the hydrodynamic performance of two-dimensional flexible carangiform swimmers with varying stiffnesses and thicknesses, which are driven by the active internal bending moments, and employ the complex orthogonal decomposition and Fourier decomposition methods to quantitatively measure and analyze the proportion of undulation. It is found that standing wave deformation characteristics are prominently observed along fish-like bodies with high stiffness, whereas traveling wave characteristics are more evident in bodies with lower stiffness. The self-propelled fish body demonstrates lateral oscillation and rotation around its center of mass, namely, the heaving and pitching movement, particularly in specimens with high stiffness. The present analysis shows that the heaving and pitching locomotion induced by the fluid significantly increase the traveling wave proportion by modulating the amplitude and phase of the left and right traveling waves viewed in forward frame. We called it fluidic undulation effects (FUE), which is different from the undulation of body deformation. This effect is more pronounced for large stiffnesses and thin airfoils. The standing wave deformation observed with a large stiffness transforms into a traveling wave propulsion pattern, with its traveling wave index even slightly surpassing that of a small-stiffness pattern. Although the efficiency of the standing wave deformation is low, it facilitates a faster forward speed (body lengths per stroke). The positive impact of the FUE on the swimming performance is also confirmed by restricting the recoil motions of the lateral translation and rotation of the body. Furthermore, we observe that there is no undulatory swimming gait that has both the highest energy efficiency and the highest speed.