Spatiotemporal Asymmetry in Metachronal Rowing at Intermediate Reynolds Numbers

Abstract

In drag-based swimming, individual propulsors operating at low Reynolds numbers (where viscous forces dominate over inertial forces) must execute a spatially asymmetric stroke to produce net fluid displacement. Temporal asymmetry (that is, differing duration between the power vs. recovery stroke) does not affect the overall generated thrust in this time-reversible regime. Metachronal rowing, in which multiple appendages beat sequentially, is used by a wide variety of organisms from low to intermediate Reynolds numbers. At the upper end of this range, inertia becomes important, and increasing temporal asymmetry can be an effective way to increase thrust. However, the combined effects of spatial and temporal asymmetry are not fully understood in the context of metachronal rowing. To explore the role of spatiotemporal asymmetry in metachronal rowing, we combine laboratory experiments and reduced-order analytical modeling. We measure beat kinematics and generated flows in two species of lobate ctenophores across a range of body sizes, from 7 to 40 mm in length. We observe characteristically different flows in ctenophores of differing body size and Reynolds number, and a general decrease in spatial asymmetry and increase in temporal asymmetry with increasing Reynolds number. We also construct a one-dimensional mathematical model consisting of a row of oscillating flat plates whose flow-normal areas change with time, and use it to explore the propulsive forces generated across a range of Reynolds numbers and kinematic parameters. The model results show that while both types of asymmetry increase force production, they have different effects in different regions of the parameter space. These results may have strong biological implications, as temporal asymmetry can be actively controlled while spatial asymmetry is likely to be partially or entirely driven by passive fluid-structure interaction.