Accelerating fishes increase propulsive efficiency by modulating vortex ring geometry

Abstract

Swimming animals need to generate propulsive force to overcome drag, regardless of whether they swim steadily or accelerate forward. While locomotion strategies for steady swimming are well characterized, far less is known about acceleration. Animals exhibit many different ways to swim steadily, but we show here that this behavioral diversity collapses into a single swimming pattern during acceleration regardless of the body size, morphology, and ecology of the animal. We draw on the fields of biomechanics, fluid dynamics, and robotics to demonstrate that there is a fundamental difference between steady swimming and forward acceleration. We provide empirical evidence that the tail of accelerating fishes can increase propulsive efficiency by enhancing thrust through the alteration of vortex ring geometry. Our study provides insight into how propulsion can be altered without increasing vortex ring size and represents a fundamental departure from our current understanding of the hydrodynamic mechanisms of acceleration. Our findings reveal a unifying hydrodynamic principle that is likely conserved in all aquatic, undulatory vertebrates.

Hydrodynamics of linear acceleration in bluegill sunfishLepomis macrochirus

“…In this case, 96 the force vector might point in the same direction as it does during steady locomotion, but the 97 total force would be greater, meaning that the axial component of the total force is also larger 98 ( Figure 1C). Akanyeti et al (2017) found that trout use both mechanisms; they produce more 99 force and they reorient it more in the axial direction. 100…”

“…The kinematics and hydrodynamics of acceleration in a variety of fish species were recently 38 surveyed (Akanyeti et al, 2017). Across 51 species, they reported a consistent, large increase in 39 tail beat amplitude and frequency.…”

“…They also studied the wake of trout in detail, and showed that 40 the kinematic changes lead to an increase in the impulse in vortex rings in the wake and a 41 reorientation of the rings, indicating that the force is reorients to be more axially directed, rather 42 than laterally. They found that the rings become more circular, which would result in a more 43 hydrodynamically efficient transfer of force into the wake (Akanyeti et al, 2017). The 44 hydrodynamics of acceleration in fishes has also been studied in American eels (Tytell, 2004a).…”

Oxygen consumption of drift-feeding rainbow trout: the energetic tradeoff between locomotion and feeding in flow

“…Compared to foraging in freestream flows, refuging fish that dart out to capture food 380 are expected to accelerate more quickly in order to overcome these velocity gradients. The large 381 amplitude kinematics of fast accelerations is significantly different than those of steady 382 swimming (Akanyeti et al 2017), and is likely the main contributor to the high energetic 383…”

The fish body functions as an airfoil: surface pressures generate thrust during carangiform locomotion

“…Presumably, timing, magnitude, and location of forces, in addition to the relative role of positive and negative pressure, could all change during accelerations. For example, many carangiform swimmers, including bluegill, have larger head and tail oscillation amplitudes and larger tailbeat frequencies during accelerations (39,47), leading to larger added masses and larger total forces (39). Interestingly, in bluegill (39) but not trout (47), these increases occur without substantially redirecting the net thrust forces relative to steady swimming, suggesting that there are differences in the force production mechanics among species and across behaviors like steady swimming and accelerations.…”