Effects of wall surge on drag-based paddling and pumping at intermediate Reynolds number

Drag-based swimming is a common locomotive strategy at low to intermediate Reynolds numbers; in this regime, organisms often use multiple flexible appendages in close proximity to modulate forces and improve efficiency. Ctenophores, a marine zooplankton and the largest known organisms to use cilia for locomotion, exemplify this strategy. These cm-scale animals propel themselves via the metachronal motion of paddle-like bundles of mm-scale cilia (ctenes), which are organized into rows along a curved body surface. In-situ observations reveal that the deformable body wall under the ctenes carries a traveling wave at the same frequency as the beating propulsors, such that the ctene base moves orthogonally to the direction of oscillation (surge). However, it remains unclear whether this substrate motion is a passive response to the pressure field generated by the overlying ctenes, or an active mechanism employed to enhance hydrodynamic performance. To evaluate the role of a surging substrate during drag-based paddling, we designed a robotic system that mimics the coupled motion of a ctene and its underlying deformable body wall. The oscillating and surging motions of a high aspect ratio paddle are controlled by a synchronized servomotor and linear actuator, respectively. A flexible sheet, deforming as the paddle surges, simulates the ctenophore’s body surface. Using Particle Image Velocimetry (PIV), we explored the hydrodynamic effects of a range of phase delays between the paddle’s oscillation and surge, as well as the orthogonal surging distance, on the generated flow. We show that the surging distance and phase delay interact to both attenuate and augment force production, depending on their timing. Significantly, the most effective phase delay for thrust augmentation in our robotic model aligns with the phase delay observed in living ctenophores. This suggests that surging substrate deformation in ctenophores may be an active component of their propulsive strategy to improve efficiency and performance. More broadly, our results emphasize the potential contribution of surging movement in drag-based swimming in general, particularly for highly flexible and deformable organisms as well as bioinspired robots, vehicles, and devices that use similar strategies.