Effect of caudal fin flexibility on the propulsive efficiency of a fish-like swimmer

Energetic benefits in coordinated circular swimming motion of two swimmers

The coordinated movement of multiple swimmers is a crucial component of fish schools. Fish swimming in different formations, such as tandem, side-by-side, diamond, and phalanx, can achieve significant energetic advantages. However, the energetic benefits of nonstraight swimming behaviors, such as the collective motion of a milling pattern, are not well understood. To fill in this gap, we consider two swimmers in circular tracks, controlled by a PID approach to reach stable configurations. Our study finds that the optimal phase is affected by circumferential effects, and that substantial energy savings can result from both propulsion and turning. We also explore the radial effect in terms of energetic benefits. In a milling pattern, the inner swimmers can easily gain a certain energetic benefit (-8%), while their peers on the outside must be close enough to the inner swimmer with a proper phase to gain the energetic benefit (-14%). When the radial spacing becomes larger or is in an unmatched phase, the swimming of the outer swimmers becomes more laborious (+16%). Our results indicate that swimmers who maintain a matched phase and minimum radial effect obtain the highest energetic benefits (-26%). These findings highlight the energetic benefits of swimmers, even in a milling pattern, where the position difference dominates the extent of benefit.

A tale of two fish tails: does a forked tail really perform better than a truncate tail when cruising?

Many fishes use their tail as the main thrust producer during swimming. This fin's diversity in shape and size influences its physical interactions with water as well as its ecological functions. Two distinct tail morphologies are common in bony fishes: flat, truncate tails which are best suited for fast accelerations via drag forces, and forked tails that promote economical, fast cruising by generating lift-based thrust. This assumption is based primarily on studies of the lunate caudal fin of Scombrids (i.e. tuna, mackerel), which is comparatively stiff and exhibits an airfoil-type cross-section. However, this is not representative of the more commonly observed and taxonomically widespread flexible forked tail, yet similar assumptions about economical cruising are widely accepted. Here, we present the first comparative experimental study of forked versus truncate tail shape and compare the fluid mechanical properties and energetics of two common nearshore fish species. We examined the hypothesis that forked tails provide a hydrodynamic advantage over truncate tails at typical cruising speeds. Using experimentally derived pressure fields, we show that the forked tail produces thrust via acceleration reaction forces like the truncate tail during cruising but at increased energetic costs. This reduced efficiency corresponds to differences in the performance of the two tail geometries and body kinematics to maintain similar overall thrust outputs. Our results offer insights into the benefits and tradeoffs of two common fish tail morphologies and shed light on the functional morphology of fish swimming to guide the development of bio-inspired underwater technologies.

Numerical modeling of a self-propelled dolphin jump out of water

A computational model is developed to investigate the jump of a self-propelled dolphin out of water. This model relies on the Navier-Stokes equations, where a fictitious domain approach with the volume penalization method is used for fluid-structure coupling, and the continuous surface force approach is used to model the water-air interface, the latter being tracked in a level-set framework. The dolphin's geometry is based on freely available data from the literature. While body deformation is imposed, the leading linear and angular displacements are computed from Newton's laws. Numerical simulations show that it is necessary to generate large propulsives forces to allow the jump out of water. When the dolphin is out of water, its trajectory follows a purely ballistic one.

Robotics as a Comparative Method in Ecology and Evolutionary Biology

Comparative biologists have typically used one or more of the following methods to assist in evaluating the proposed functional and performance significance of individual traits: comparative phylogenetic analysis, direct interspecific comparison among species, genetic modification, experimental alteration of morphology (for example by surgically modifying traits), and ecological manipulation where individual organisms are transplanted to a different environment. But comparing organisms as the endpoints of an evolutionary process involves the ceteris paribus assumption: that all traits other than the one(s) of interest are held constant. In a properly controlled experimental study, only the variable of interest changes among the groups being compared. The theme of this paper is that the use of robotic or mechanical models offers an additional tool in comparative biology that helps to minimize the effect of uncontrolled variables by allowing direct manipulation of the trait of interest against a constant background. The structure and movement pattern of mechanical devices can be altered in ways not possible in studies of living animals, facilitating testing hypotheses of the functional and performance significant of individual traits. Robotic models of organismal design are particularly useful in three arenas: (1) controlling variation to allow modification only of the trait of interest, (2) the direct measurement of energetic costs of individual traits, and (3) quantification of the performance landscape. Obtaining data in these three areas is extremely difficult through the study of living organisms alone, and the use of robotic models can reveal unexpected effects. Controlling for all variables except for the length of a swimming flexible object reveals substantial non-linear effects that vary with stiffness. Quantification of the swimming performance surface reveals that there are two peaks with comparable efficiency, greatly complicating the inference of performance from morphology alone. Organisms and their ecological interactions are complex, and dissecting this complexity to understand the effects of individual traits is a grand challenge in ecology and evolutionary biology. Robotics has great promise as a "comparative method," allowing better-controlled comparative studies to analyze the many interacting elements that make up complex behaviors, ecological interactions, and evolutionary histories.

Computational modeling of swimming in marine invertebrates with implications for soft swimming robots

Marine flatworms (polyclads) employ a wide variety of body kinematics for swimming. In the current study, we employ computational fluid dynamics to study the hydrodynamics and swimming performance of a large variety of swimmers inspired directly from flatworms as well as two other marine invertebrates: Aplysia and Spanish dancers. The free-swimming performance is evaluated via two metrics: Froude efficiency and terminal swimming speed. The study examines the effect of the flapping of the lateral margins of the body as well as body undulation, which are used in various combinations by these animals to achieve swimming. The simulations suggest that a spanwise compact wake with distinct vortex ring structures is well correlated with a high swimming performance. We find that the addition of even a small magnitude of body undulation to lateral flapping results in significant changes in the wake patterns and noticeable improvements in the swimming performance compared to swimmers that employ only lateral flapping. Periodic body-bending synchronized with lateral flapping, as employed by the Spanish dancer, is found to be a very effective swimming gait. Some gaits that employ body undulations but no lateral flapping are found to generate high swimming speeds but with limited swimming efficiencies. Taken together, this study provides insights that could inform the design of swimming robots.

Swimming without a spine: computational modeling and analysis of the swimming hydrodynamics of the Spanish Dancer

Incompressible flow simulations are used to study the swimming of a Spanish Dancer (Hexabranchus sanguineus), a soft-bodied invertebrate marine gastropod that swims by combining body pitching with undulations of its large mantle. A simple model based on a field video is employed as the basis for the model and coupling of the flow with the body acceleration enables us to examine the free swimming of this animal. Simulations indicate propulsive efficiencies up to about 57% and terminal swimming speeds of 1.33 body lengths per cycle. Examination of the effect of body planform on the swimming hydrodynamics suggests that the planform of this animal is likely adapted to enhance its swimming performance.

Suction-based propulsion as a basis for efficient animal swimming

A central and long-standing tenet in the conceptualization of animal swimming is the idea that propulsive thrust is generated by pushing the surrounding water rearward. Inherent in this perspective is the assumption that locomotion involves the generation of locally elevated pressures in the fluid to achieve the expected downstream push of the surrounding water mass. Here we show that rather than pushing against the surrounding fluid, efficient swimming animals primarily pull themselves through the water via suction. This distinction is manifested in dominant low-pressure regions generated in the fluid surrounding the animal body, which are observed by using particle image velocimetry and a pressure calculation algorithm applied to freely swimming lampreys and jellyfish. These results suggest a rethinking of the evolutionary adaptations observed in swimming animals as well as the mechanistic basis for bio-inspired and biomimetic engineered vehicles.

Swimming animals are generally assumed to generate forward thrust by pushing surrounding water rearwards. Here, Gemmell et al. show that efficient swimming in lampreys and jellyfish is achieved primarily through suction, as vortex-associated low pressure regions are synchronized by undulations of the body.

Efficiency of fish propulsion

The system efficiency of a self-propelled flexible body is ill-defined, hence we introduce the concept of quasi-propulsive efficiency, defined as the ratio of the power needed to tow a body in rigid-straight condition over the power it requires for self-propulsion, both measured for the same speed. Through examples we show that the quasi-propulsive efficiency is a rational non-dimensional metric of the propulsive fitness of fish and fish-like mechanisms, consistent with the goal to minimize fuel consumption under size and velocity constraints. We perform two-dimensional viscous simulations and apply the concept of quasi-propulsive efficiency to illustrate and discuss the efficiency of two-dimensional undulating foils employing first carangiform and then anguilliform kinematics. We show that low efficiency may be due to adverse body-propulsor hydrodynamic interactions, which cannot be accounted for by an increase in friction drag, as done previously, since at the Reynolds number Re = 5 000 considered in the simulations, pressure is a major contributor to both thrust and drag.

Performance of synchronized fins in biomimetic propulsion

By using a two-dimensional model of ray fins, we numerically investigate the thrust generation by closely-coupled fins with an immersed boundary approach. The concentration is on the performance enhancement through fin-fin interactions and the underlying vortex control mechanisms in three representative systems, a two-fin tandem configuration, a two-fin parallel configuration, and a three-fin triangular configuration. In all these systems the thrust generation can be significantly increased in comparison with single fins. Unlike previous studies of tandem fins, in which the gap and phase lag between the two fins were considered separately, our study shows that the dynamics of the system is determined by a parameter that combines these two (the global phase difference). The optimal performance occurs as this parameter is around π (destructive mode), and the worst performance occurs when it is around 0 (constructive mode). Interestingly, contrary to the vorticity cancellation scenario implied by its name, our simulations show that in the destructive mode there is in fact a wake re-organization mechanism, during which vortices with the same rotational direction shed from the two fins are attracted towards each other and merge. Subsequently, the wake downstream becomes a strong and well-organized reverse Kármán vortex street, which explains the increased thrust. In the parallel system, the best performance occurs in cases when the two fins are in opposites phases. Both the thrust and efficiency increase as the gap between the fins decreases, until a symmetry-breaking instability occurs in the wake and the efficiency starts plunging due to the increase in lateral force generation. In the triangular formation, the highest thrust generation also occurs in the destructive mode. However, no further increase in performance is observed compared with the tandem system.