Cost of Transport of Undulating Fin Propulsion.

Autonomous robots are used to inspect, repair and maintain underwater assets. These tasks require energy-efficient robots, including efficient movement to extend available operational time. To examine the suitability of a propulsion system based on undulating fins, we built two robots with one and two fins, respectively, and conducted a parametric study for combinations of frequency, amplitude, wavenumber and fin shapes in free-swimming experiments, measuring steady-state swimming speed, power consumption and cost of transport. The following trends emerged for both robots. Swimming speed was more strongly affected by frequency than amplitude across the examined wavenumbers and fin heights. Power consumption was sensitive to frequency at low wavenumbers, and increasingly sensitive to amplitude at high wavenumbers. This increasing sensitivity of amplitude was more pronounced in tall rather than short fins. Cost of transport showed a complex relation with fin size and kinematics and changed drastically across the mapped parameter space. At equal fin kinematics as the single-finned robot, the double-finned robot swam slightly faster (>10%) with slightly lower power consumption (<20%) and cost of transport (<40%). Overall, the robots perform similarly to finned biological swimmers and other bio-inspired robots, but do not outperform robots with conventional propulsion systems.

Fishes regulate tail-beat kinematics to minimize speed-specific cost of transport.

Energetic expenditure is an important factor in animal locomotion. Here we test the hypothesis that fishes control tail-beat kinematics to optimize energetic expenditure during undulatory swimming. We focus on two energetic indices used in swimming hydrodynamics, cost of transport and Froude efficiency. To rule out one index in favour of another, we use computational-fluid dynamics models to compare experimentally observed fish kinematics with predicted performance landscapes and identify energy-optimized kinematics for a carangiform swimmer, an anguilliform swimmer and larval fishes. By locating the areas in the predicted performance landscapes that are occupied by actual fishes, we found that fishes use combinations of tail-beat frequency and amplitude that minimize cost of transport. This energy-optimizing strategy also explains why fishes increase frequency rather than amplitude to swim faster, and why fishes swim within a narrow range of Strouhal numbers. By quantifying how undulatory-wave kinematics affect thrust, drag, and power, we explain why amplitude and frequency are not equivalent in speed control, and why Froude efficiency is not a reliable energetic indicator. These insights may inspire future research in aquatic organisms and bioinspired robotics using undulatory propulsion.

Complexity and diversity of motion amplification and control strategies in motile carnivorous plant traps.

Similar to animals, plants have evolved mechanisms for elastic energy storage and release to power and control rapid motion, yet both groups have been largely studied in isolation. This is exacerbated by the lack of consistent terminology and conceptual frameworks describing elastically powered motion in both groups. Iconic examples of fast movements can be found in carnivorous plants, which have become important models to study biomechanics, developmental processes, evolution and ecology. Trapping structures and processes vary considerably between different carnivorous plant groups. Using snap traps, suction traps and springboard-pitfall traps as examples, we illustrate how traps mix and match various mechanisms to power, trigger and actuate motions that contribute to prey capture, retention and digestion. We highlight a fundamental trade-off between energetic investment and movement control and discuss it in a functional-ecological context.

Form, Structure, and Function: How Plants vs. Animals Solve Physical Problems.

Plants and animals have evolved solutions for a wide range of mechanical problems, such as adhesion and dispersal. Several of these solutions have been sources for bio-inspiration, like the Lotus Effect for self-cleaning surfaces or Velcro for adhesion. This symposium brought together plant and animal biomechanics researchers who tackle similar problems in different systems under the unifying theme of structure-function relations with relevance to bio-inspiration. For both communities it holds true that the structural systems, which have evolved in the respective organisms to address the mechanical challenges mentioned above, are often highly complex. This requires interdisciplinary research involving "classical" experimental biology approaches in combination with advanced imaging methods and computational modeling. The transfer of such systems into biomimetic technical materials and structures comes with even more challenges, like scalability issues and applicability. Having brought all these topics under one umbrella, this symposium presented the forefront of biophysical basic and application-oriented international research with the goal of facilitation knowledge transfer across systems and disciplines.

Suction Feeding by Small Organisms: Performance Limits in Larval Vertebrates and Carnivorous Plants.

Suction feeding has evolved independently in two highly disparate animal and plant systems, aquatic vertebrates and carnivorous bladderworts. We review the suction performance of animal and plant suction feeders to explore biomechanical performance limits for aquatic feeders based on morphology and kinematics, in the context of current knowledge of suction feeding. While vertebrates have the greatest diversity and size range of suction feeders, bladderworts are the smallest and fastest known suction feeders. Body size has profound effects on aquatic organismal function, including suction feeding, particularly in the intermediate flow regime that tiny organisms can experience. A minority of tiny organisms suction feed, consistent with model predictions that generating effective suction flow is less energetically efficient and also requires more flow-rate specific power at small size. Although the speed of suction flows generally increases with body and gape size, some specialized tiny plant and animal predators generate suction flows greater than those of suction feeders 100 times larger. Bladderworts generate rapid flow via high-energy and high-power elastic recoil and suction feed for nutrients (relying on photosynthesis for energy). Small animals may be limited by available muscle energy and power, although mouth protrusion can offset the performance cost of not generating high suction pressure. We hypothesize that both the high energetic costs and high power requirements of generating rapid suction flow shape the biomechanics of small suction feeders, and that plants and animals have arrived at different solutions due in part to their different energy budgets.

Bladderworts, the smallest known suction feeders, generate inertia-dominated flows to capture prey.

Aquatic bladderworts (Utricularia gibba and U. australis) capture zooplankton in mechanically triggered underwater traps. With characteristic dimensions less than 1 mm, the trapping structures are among the smallest known to capture prey by suction, a mechanism that is not effective in the creeping-flow regime where viscous forces prevent the generation of fast and energy-efficient suction flows. To understand what makes suction feeding possible on the small scale of bladderwort traps, we characterised their suction flows experimentally (using particle image velocimetry) and mathematically (using computational fluid dynamics and analytical mathematical models). We show that bladderwort traps avoid the adverse effects of creeping flow by generating strong, fast-onset suction pressures. Our findings suggest that traps use three morphological adaptations: the trap walls' fast release of elastic energy ensures strong and constant suction pressure; the trap door's fast opening ensures effectively instantaneous onset of suction; the short channel leading into the trap ensures undeveloped flow, which maintains a wide effective channel diameter. Bladderwort traps generate much stronger suction flows than larval fish with similar gape sizes because of the traps' considerably stronger suction pressures. However, bladderworts' ability to generate strong suction flows comes at considerable energetic expense.

Mechanical Ecology-Taking Biomechanics to the Field.

Synopsis Interdisciplinary research can have strong and surprising synergistic effects, leading to rapid knowledge gains. Equally important, it can help to reintegrate fragmented fields across increasingly isolated specialist sub-disciplines. However, the lack of a common identifier for research "in between fields" can make it difficult to find relevant research outputs and network effectively. We illustrate and address this issue for the emerging interdisciplinary hotspot of "mechanical ecology," which we define here as the intersection of quantitative biomechanics and field ecology at the organism level. We show that an integrative approach crucially advances our understanding in both disciplines by (1) putting biomechanical mechanisms into a biologically meaningful ecological context and (2) addressing the largely neglected influence of mechanical factors in organismal and behavioral ecology. We call for the foundation of knowledge exchange platforms such as meeting symposia, special issues in journals, and focus groups dedicated to mechanical ecology.

Hydrodynamics of the bladderwort feeding strike.

The aquatic bladderwort Utricularia gibba captures zooplankton in mechanically triggered underwater traps. With characteristic dimensions <1 mm, the trapping structures are among the smallest known that work by suction-a mechanism that would not be effective in the creeping-flow regime. To understand the adaptations that make suction feeding possible on this small scale, we have measured internal flow speeds during artificially triggered feeding strikes in the absence of prey. These data are compared with complementary analytical models of the suction event: an inviscid model of the jet development in time and a steady-state model incorporating friction. The initial dynamics are well described by a time-dependent Bernoulli equation in which the action of the trap door is represented by a step increase in driving pressure. According to this model, the observed maximum flow speed (5.2 m/s) depends only on the pressure difference, whereas the initial acceleration (3 × 104 m/s2 ) is determined by pressure difference and channel length. Because the terminal speed is achieved quickly (~0.2 ms) and the channel is short, the remainder of the suction event (~2.0 ms) is effectively an undeveloped viscous steady state. The steady-state model predicts that only 17% of power is lost to friction. The energy efficiency and steady-state fluid speed decrease rapidly with decreasing channel diameter, setting a lower limit on practical bladderwort size.

Thermodynamics of the Bladderwort Feeding Strike-Suction Power from Elastic Energy Storage.

The carnivorous plant bladderwort exemplifies the use of accumulated elastic energy to power motion: respiration-driven pumps slowly load the walls of its suction traps with elastic energy (∼1 h). During a feeding strike, this energy is released suddenly to accelerate water (∼1 ms). However, due to the traps' small size and concomitant low Reynolds number, a significant fraction of the stored energy may be dissipated as viscous friction. Such losses and the mechanical reversibility of Stokes flow are thought to degrade the feeding success of other suction feeders in this size range, such as larval fish. In contrast, triggered bladderwort traps are generally successful. By mapping the energy budget of a bladderwort feeding strike, we illustrate how this smallest of suction feeders can perform like an adult fish.

Data Management Rubric for Video Data in Organismal Biology.

SYNOPSIS: Standards-based data management facilitates data preservation, discoverability, and access for effective data reuse within research groups and across communities of researchers. Data sharing requires community consensus on standards for data management, such as storage and formats for digital data preservation, metadata (i.e., contextual data about the data) that should be recorded and stored, and data access. Video imaging is a valuable tool for measuring time-varying phenotypes in organismal biology, with particular application for research in functional morphology, comparative biomechanics, and animal behavior. The raw data are the videos, but videos alone are not sufficient for scientific analysis. Nearly endless videos of animals can be found on YouTube and elsewhere on the web, but these videos have little value for scientific analysis because essential metadata such as true frame rate, spatial calibration, genus and species, weight, age, etc. of organisms, are generally unknown. We have embarked on a project to build community consensus on video data management and metadata standards for organismal biology research. We collected input from colleagues at early stages, organized an open workshop, "Establishing Standards for Video Data Management," at the Society for Integrative and Comparative Biology meeting in January 2017, and then collected two more rounds of input on revised versions of the standards. The result we present here is a rubric consisting of nine standards for video data management, with three levels within each standard: good, better, and best practices. The nine standards are: (1) data storage; (2) video file formats; (3) metadata linkage; (4) video data and metadata access; (5) contact information and acceptable use; (6) camera settings; (7) organism(s); (8) recording conditions; and (9) subject matter/topic. The first four standards address data preservation and interoperability for sharing, whereas standards 5-9 establish minimum metadata standards for organismal biology video, and suggest additional metadata that may be useful for some studies. This rubric was developed with substantial input from researchers and students, but still should be viewed as a living document that should be further refined and updated as technology and research practices change. The audience for these standards includes researchers, journals, and granting agencies, and also the developers and curators of databases that may contribute to video data sharing efforts. We offer this project as an example of building community consensus for data management, preservation, and sharing standards, which may be useful for future efforts by the organismal biology research community.

Fish larvae exploit edge vortices along their dorsal and ventral fin folds to propel themselves.

Larvae of bony fish swim in the intermediate Reynolds number (Re) regime, using body- and caudal-fin undulation to propel themselves. They share a median fin fold that transforms into separate median fins as they grow into juveniles. The fin fold was suggested to be an adaption for locomotion in the intermediate Reynolds regime, but its fluid-dynamic role is still enigmatic. Using three-dimensional fluid-dynamic computations, we quantified the swimming trajectory from body-shape changes during cyclic swimming of larval fish. We predicted unsteady vortices around the upper and lower edges of the fin fold, and identified similar vortices around real larvae with particle image velocimetry. We show that thrust contributions on the body peak adjacent to the upper and lower edges of the fin fold where large left-right pressure differences occur in concert with the periodical generation and shedding of edge vortices. The fin fold enhances effective flow separation and drag-based thrust. Along the body, net thrust is generated in multiple zones posterior to the centre of mass. Counterfactual simulations exploring the effect of having a fin fold across a range of Reynolds numbers show that the fin fold helps larvae achieve high swimming speeds, yet requires high power. We conclude that propulsion in larval fish partly relies on unsteady high-intensity vortices along the upper and lower edges of the fin fold, providing a functional explanation for the omnipresence of the fin fold in bony-fish larvae.

How body torque and Strouhal number change with swimming speed and developmental stage in larval zebrafish.

Small undulatory swimmers such as larval zebrafish experience both inertial and viscous forces, the relative importance of which is indicated by the Reynolds number (Re). Re is proportional to swimming speed (vswim) and body length; faster swimming reduces the relative effect of viscous forces. Compared with adults, larval fish experience relatively high (mainly viscous) drag during cyclic swimming. To enhance thrust to an equally high level, they must employ a high product of tail-beat frequency and (peak-to-peak) amplitude fAtail, resulting in a relatively high fAtail/vswim ratio (Strouhal number, St), and implying relatively high lateral momentum shedding and low propulsive efficiency. Using kinematic and inverse-dynamics analyses, we studied cyclic swimming of larval zebrafish aged 2-5 days post-fertilization (dpf). Larvae at 4-5 dpf reach higher f (95 Hz) and Atail (2.4 mm) than at 2 dpf (80 Hz, 1.8 mm), increasing swimming speed and Re, indicating increasing muscle powers. As Re increases (60 → 1400), St (2.5 → 0.72) decreases nonlinearly towards values of large swimmers (0.2-0.6), indicating increased propulsive efficiency with vswim and age. Swimming at high St is associated with high-amplitude body torques and rotations. Low propulsive efficiencies and large yawing amplitudes are unavoidable physical constraints for small undulatory swimmers.

Refraction corrected calibration for aquatic locomotion research: application of Snell's law improves spatial accuracy.

Images of underwater objects are distorted by refraction at the water-glass-air interfaces and these distortions can lead to substantial errors when reconstructing the objects' position and shape. So far, aquatic locomotion studies have minimized refraction in their experimental setups and used the direct linear transform algorithm (DLT) to reconstruct position information, which does not model refraction explicitly. Here we present a refraction corrected ray-tracing algorithm (RCRT) that reconstructs position information using Snell's law. We validated this reconstruction by calculating 3D reconstruction error-the difference between actual and reconstructed position of a marker. We found that reconstruction error is small (typically less than 1%). Compared with the DLT algorithm, the RCRT has overall lower reconstruction errors, especially outside the calibration volume, and errors are essentially insensitive to camera position and orientation and the number and position of the calibration points. To demonstrate the effectiveness of the RCRT, we tracked an anatomical marker on a seahorse recorded with four cameras to reconstruct the swimming trajectory for six different camera configurations. The RCRT algorithm is accurate and robust and it allows cameras to be oriented at large angles of incidence and facilitates the development of accurate tracking algorithms to quantify aquatic manoeuvers.

Escape trajectories are deflected when fish larvae intercept their own C-start wake.

Fish larvae may intercept their own wake during sharp turns, which might affect their escape performance. We analysed C-starts of larval zebrafish (Danio rerio, Hamilton, 1822) using a computational fluid dynamics approach that simulates free swimming (swimming trajectory is determined by fluid forces) by coupling hydrodynamics and body dynamics. The simulations show that fish may intercept their own wake when they turn by 100-180°. During stage 1 of a C-start, the fish generates a strong jet at the tail that is shed into the wake. During stage 2, the fish intercepts this wake. Counterfactual simulations showed that wake interception increased the lateral force on the fish and reduced the fish's turning angle by more than 5°. Wake interception caused no significant acceleration tangential to the trajectory of the fish and did not affect total power output. While experimental and simulation evidence suggests that fish larvae can either undershoot or intercept but not overshoot their wake, our simulations show that larger fish might be able to avoid intercepting their wake by either under- or overshooting. As intercepting its own wake modifies the fish's escape trajectory, fish should account for this effect when planning their escape route.

Body dynamics and hydrodynamics of swimming fish larvae: a computational study.

To understand the mechanics of fish swimming, we need to know the forces exerted by the fluid and how these forces affect the motion of the fish. To this end, we developed a 3-D computational approach that integrates hydrodynamics and body dynamics. This study quantifies the flow around a swimming zebrafish (Danio rerio) larva. We used morphological and kinematics data from actual fish larvae aged 3 and 5 days post fertilization as input for a computational model that predicted free-swimming dynamics from prescribed changes in body shape. We simulated cyclic swimming and a spontaneous C-start. A rigorous comparison with 2-D particle image velocimetry and kinematics data revealed that the computational model accurately predicted the motion of the fish's centre of mass as well as the spatial and temporal characteristics of the flow. The distribution of pressure and shear forces along the body showed that thrust is mainly produced in the posterior half of the body. We also explored the effect of the body wave amplitude on swimming performance by considering wave amplitudes that were up to 40% larger or smaller than the experimentally observed value. Increasing the body wave amplitude increased forward swimming speed from 7 to 21 body lengths per second, which is consistent with experimental observations. The model also predicted a non-linear increase in propulsive efficiency from 0.22 to 0.32 while the required mechanical power quadrupled. The efficiency increase was only minor for wave amplitudes above the experimental reference value, whereas the cost of transport rose significantly.

Automated visual tracking for studying the ontogeny of zebrafish swimming.

The zebrafish Danio rerio is a widely used model organism in studies of genetics, developmental biology, and recently, biomechanics. In order to quantify changes in swimming during all stages of development, we have developed a visual tracking system that estimates the posture of fish. Our current approach assumes planar motion of the fish, given image sequences taken from a top view. An accurate geometric fish model is automatically designed and fit to the images at each time frame. Our approach works across a range of fish shapes and sizes and is therefore well suited for studying the ontogeny of fish swimming, while also being robust to common environmental occlusions. Our current analysis focuses on measuring the influence of vertebra development on the swimming capabilities of zebrafish. We examine wild-type zebrafish and mutants with stiff vertebrae (stocksteif) and quantify their body kinematics as a function of their development from larvae to adult (mutants made available by the Hubrecht laboratory, The Netherlands). By tracking the fish, we are able to measure the curvature and net acceleration along the body that result from the fish's body wave. Here, we demonstrate the capabilities of the tracking system for the escape response of wild-type zebrafish and stocksteif mutant zebrafish. The response was filmed with a digital high-speed camera at 1500 frames s(-1). Our approach enables biomechanists and ethologists to process much larger datasets than possible at present. Our automated tracking scheme can therefore accelerate insight in the swimming behavior of many species of (developing) fish.

Flow patterns of larval fish: undulatory swimming in the intermediate flow regime.

Fish larvae, like many adult fish, swim by undulating their body. However, their body size and swimming speeds put them in the intermediate flow regime, where viscous and inertial forces both play an important role in the interaction between fish and water. To study the influence of the relatively high viscous forces compared with adult fish, we mapped the flow around swimming zebrafish (Danio rerio) larvae using two-dimensional digital particle image velocimetry (2D-DPIV) in the horizontal and transverse plane of the fish. Fish larvae initiate a swimming bout by bending their body into a C shape. During this initial tail-beat cycle, larvae shed two vortex pairs in the horizontal plane of their wake, one during the preparatory and one during the subsequent propulsive stroke. When they swim ;cyclically' (mean swimming speed does not change significantly between tail beats), fish larvae generate a wide drag wake along their head and anterior body. The flow along the posterior body is dominated by the undulating body movements that cause jet flows into the concave bends of the body wave. Patches of elevated vorticity form around the jets, and travel posteriorly along with the body wave, until they are ultimately shed at the tail near the moment of stroke reversal. Behind the larva, two vortex pairs are formed per tail-beat cycle (the tail beating once left-to-right and then right-to-left) in the horizontal plane of the larval wake. By combining transverse and horizontal cross sections of the wake, we inferred that the wake behind a cyclically swimming zebrafish larva contains two diverging rows of vortex rings to the left and right of the mean path of motion, resembling the wake of steadily swimming adult eels. When the fish larva slows down at the end of a swimming bout, it gradually reduces its tail-beat frequency and amplitude, while the separated boundary layer and drag wake of the anterior body extend posteriorly to envelope the entire larva. This drag wake is considerably wider than the larval body. The effects of the intermediate flow regime manifest as a thick boundary layer and in the quick dying-off of the larval wake within less than half a second.