The goal of this study was to examine the fluid flows directly adjacent to propulsor surfaces in order to better understand how metachronal propulsors interact with fluids for thrust production. Based on the direct comparison of the mean contributions of pulling vs. pushing forces throughout the power stroke of replicate individual propulsors (Fig. 4, which are generated by negative vs. positive pressure fields, respectively) we suggest that the propulsors of the animals examined rely predominantly on negative pressure for generating thrust. The assertion that these propulsor level observations to apply to the movement of the whole animal requires the assumptions that, first, the propulsors we quantified are representative of the all the other propulsors contributing to swimming thrust, and second, that the thrust generated for the whole animal is due to accumulated total thrust generated by individual propulsors. Although our data addresses the first of these assumptions by replicating individual propulsors, we cannot document the second assumption that the total thrust represents the sum of all individual propulsor elements. While this second assumption is intuitively appealing, our data is confined to the small spatial and temporal scales around individual propulsor elements. Confirmation that the whole-organism thrust results from of the summation of individual contributions requires experiments at different scales than those used in the current study.
Thrust generated by a propulsor is ultimately determined by the overall pressure gradient across the propulsor. So does it matter whether that gradient is dominated by negative or positive pressure? We believe that this distinction is fundamental for understanding why animal propulsors bend in a surprisingly characteristic and narrow range. Rigid paddle designs are dominated by positive pressure pushing against a fluid, which in turn, generates thrust pushing a body forward. Bending at propulsor margins encourages vortex formation on the lee side of the propulsor (Figs. 2, 3) that differs from rigid propulsors. Counter-rotating vortices formed on the lee side of a bending propulsor accelerate fluid at the intersection of the vortices12,15. The fluid thus accelerated relative to the leading edge of the propulsor is the basis of the pressure gradient across the propulsor surface. In turn, this elevated pressure gradient generates high thrust and is the reason for the dominant contribution of suction thrust to natural bending propulsors. More generally, negative pressure fields are a fundamental feature of vortices which are universally formed around objects moving in fluids (except at the lowest Reynolds numbers). Lift, a different propulsive mode that relies on negative pressure, is a well-known example that illustrates how kinematics and morphology can enhance negative pressure for thrust2. Lift occurs when a foil separates flow traveling over and under the foil surface. With the correct foil shape and kinematics, the separation of flow can generate strong negative pressure fields above the foil leading to an upward pulling thrust on the foil. This lift relies on the negative pressure field and foil shape.
To be clear, the thrust generated by limbs and ctenes in this study is not lift because the forces generated by lift are directed perpendicular to the direction of flow and the forces we describe are oriented in the direction of flow (Fig. 3). However, like lift, we suggest that paddles must move with prescribed kinematics to generate enhanced negative pressure fields. Bending kinematics in particular have been shown to greatly enhance vorticity and along with that, negative pressure11,16,17. Rigid, non-bending paddles generate different hydrodynamic structures than we observed13,14 and do not generate strong negative pressure fields16,17,18,19. Therefore, the kinematics of bending appear to be important for generating strong negative pressure fields around moving propulsors.
Until recently, technical constraints have limited our ability to investigate the scope of the benefits of using negative pressure for thrust. However several numerical studies, and a few experimental studies, have compared rigid to flexible propulsors. These studies have demonstrated that first, bending enhances negative pressure fields, second, bending generates elevated thrust, and third, bending enhances hydrodynamic efficiency12,16,17,20,21,22,23,24. The hydrodynamic patterns around bending propulsors show that negative pressure fields associated with bends generate significantly greater flow velocities than positive pressure fields (Fig. 2e11,12,16,21). This would lead to enhanced momentum transfer and explain the enhanced thrust observed for bending propulsors. The similar bending kinematics between the limbs and ctenes in this study and the swimming and flying animals from Lucas et al.1 suggests that these small paddling swimmers may employ similar hydrodynamic features as flying birds and swimming fish. If these bending patterns are predominately used to generate negative pressure fields for thrust, it follows that there is a need for greater focus on negative pressure around bending propulsors in order to understand the extent of the benefits of animals experience by pulling rather than pushing themselves through fluids.
Despite the vast difference in scale and Reynolds number, the results of this study suggest that the small metachronal paddles of swimming invertebrates may produce some similar effects as flapping wings in birds and insects. For example, there are similarities in the degree of bending and location of bending for the paddles in this study and the spanwise flexibility of birds and insects1. Such spanwise flexibility was found to be beneficial and yielded an increase in thrust coefficient, and a small decrease in power-input requirement, resulting in higher efficiency25.
In addition to the benefits for single propulsors, negative pressure fields can facilitate the movement and coordination of multiple propulsors which have antiplectic metachronal wave kinematics. During an antiplectic metachronal wave, a leading propulsor will begin the power stroke and, after it has initiated its stroke, the propulsor immediately behind it will initiate its own power stroke. This sequential pattern will continue for all the subsequent propulsors in the antiplectic wave. The predominately negative pressure on the leeward of each propulsor can serve to facilitate the kinematics of the adjacent propulsor by reducing the hydrodynamic resistance necessary to initiate and complete its power stroke26. In addition, the negative pressure in the gap between adjacent propulsors can serve as a cue for the adjacent propulsor to initiate its power stroke. It has been suggested that the ctenes of ctenophores require such cues to coordinate the metachronal kinematics26,27,28. At lower Reynolds numbers (Re < 10–2 versus the 101 we observed), adjacent cilia have been shown to be hydrodynamically synchronized29. Although the role of negative pressure at these Re have not been investigated, negative pressure may serve as the hydrodynamic mechanism that coordinates these propulsors as well as those at higher Re levels. It may be possible that antiplectic metachronal waves inherently depend upon negative pressure and that the predominance of antiplectic waves in multi-unit propulsors may result from the predominance of negative pressure fields that assist coordination of multi-unit propulsors.
The limbs and ctenes of small invertebrates rely on the generation of negative pressure fields for thrust production and their bending kinematics conform to the bending patterns observed among a vast array of swimming and flying animals. This may reflect the fact that a subtle bend (< 30% inflexion) appears to generate a cascade of hydrodynamic effects which enhance formation of negative pressure regions around propulsors and, ultimately, lead to enhanced thrust and hydrodynamic efficiency. These enhancements appear to be optimized for small bends20,21. Invertebrate animals with multiple paddles can coordinate the sequential build-up of negative pressure fields along antiplectic metachronally moving limbs for an additive thrust benefit and to facilitate the coordination of the sequential propulsors.
Source: Ecology - nature.com
