Force scaling and efficiency of elongated median fin propulsion.

Several fishes swim by undulating a thin and elongated median fin while the body is mostly kept straight, allowing them to perform forward and directional maneuvers. We used a robotic vessel with similar fin propulsion to determine the thrust scaling and efficiency. Using precise force and swimming kinematics measurements with the robotic vessel, the thrust generated by the undulating fin was found to scale with the square of the relative velocity between the free streaming flow and the wave speed. A hydrodynamic efficiency is presented based on propulsive force measurements and modelling of the power required to oscillate the fin laterally. It was found that the propulsive efficiency has a broadly high performance versus swimming speed, with a maximum efficiency of 75%. An expression to calculate the swimming speed over wave speed was found to depend on two parameters:Ap/Ae(ratio between body frontal area to fin swept area) andCD/Cx(ratio of body drag to fin thrust coefficient). The models used to calculate propulsive force and free-swimming speed were compared with experimental results. The broader impacts of these results are discussed in relation to morphology and the function of undulating fin swimmers. In particular, we suggest that the ratio of fin and body height found in natural swimmers could be due to a trade-off between swimming efficiency and swimming speed.

Mangrove roots model suggest an optimal porosity to prevent erosion.

Mangrove swamps are extremely productive ecosystems providing many ecological services in coastal regions. The hydrodynamic interactions of mangrove roots and water flow have been proposed as a key element to mitigate erosion. Several studies reveal that precise prediction of the morphological evolution of coastal areas, in the face of global warming and the consequent sea-level rise, requires an understanding of interactions between root porosity (the fraction of the volume of void space over the total volume), water flows, and sediment transport. Water flows around the mangrove prop roots create a complex energetic process that mixes up sediments and generates a depositional region posterior to the roots. In this work, we investigated the boundary layer behind permeable arrays of cylinders (patch) that represent the mangrove roots to explore the impact of patch porosity on the onset of sediment transport. The flow measurements were performed in a vertical plane along the water depth downstream of the mangrove root models. A high-resolution Particle Image Velocimetry (PIV) was used in a flume to observe the impact of porosity on the mean flow, velocity derivatives, skin friction coefficient, and production of turbulent kinetic energy for Reynolds number of 2500 (based on patch diameter length-scale). Here, we proposed a predictive model for critical velocity for incipient motion that takes into account the mangrove roots porosity and the near-bed turbulence effect. It is found that the patch with the [Formula: see text] porosity, has the maximum critical velocity over which the sediment transport initiates. We found the optimum porosity has the minimum sediment erosion and creates negative vorticity sources near the bed that increases the critical velocity. This signifies an optimum porosity for the onset of sediment transport consistent with the porosity of mangroves in nature. The phenomenological model is elucidated based on an analysis of the vorticity evolution equation for viscous incompressible flows. For the optimum porous patch, a sink of vorticity was formed which yielded to lower the near-bed turbulence and vorticity. The minimum velocity fluctuations were sufficient to initiate the boundary layer transition, however, the viscous dissipation dominated the turbulence production to obstruct the sediment transport. This work identified the pivotal role of mangrove root porosity in sediment transport in terms of velocity and its derivatives in wall-bounded flows. Our work also provides insight into the sediment transport and erosion processes that govern the evolution of the shapes of shorelines.

Robotic device shows lack of momentum enhancement for gymnotiform swimmers.

Many fish generate thrust by undulating one or multiple elongated fins while keeping their body straight. This propulsion mechanism has stimulated interest in both biology and bio-inspired marine propulsion because its maneuverability and efficiency at low speed. Analytical studies have found that a fin attached to a rigid flat body can produce substantially higher thrust compared to a fin without a body, three- to four-fold for natural swimmers. However, this momentum enhancement has not been confirmed experimentally. In this work, a robotic ribbon fin model with an adjustable-height body was used to test the momentum enhancement for gymontiform swimmers where the undulating fin runs along the ventral side of the body. In a series of experiments, the force generated by the robotic device was measured as the body height of the robot, the undulating fin frequency and the flow speed were changed. It was found that the thrust generated by the ribbon fin is not affected by the presence of a body, thereby resulting in no momentum enhancement due to the fin-body interaction. These results suggest that if there is a benefit at a specific fin-body height ratio of the fishes, the momentum enhancement is not the reason. This result has broader implications in understanding the evolutionary adaption of undulatory fin propulsion and underwater vehicles designs.

Design and assessment of a flexible fish robot actuated by shape memory alloys.

In this paper, we present a fish-like underwater robot inspired by the black bass fish. This robot is composed of a deformable structure and muscle-like linear actuators based on shape memory alloy wires. Such actuators are used to bend a continuous structure representing the backbone of the fish. The prototype is also equipped with a bio-inspired synthetic skin made of liquid silicone rubber and Lycra microfiber mesh. We present the mechatronics of the prototype and its control scheme, which take advantage of flex sensors for proprioception. Experiments under different conditions (in air and in water) assess the effectiveness of the mechatronics design and demonstrate that a relatively simple PID controller provides high precision of the muscles' position control. Here, the implementation of biomimetic kinematics and silent actuation technology in bio-inspired underwater robotics are demonstrated. Progress in this technology could provide multiple applications, including fish farming, coastal protection and live animal monitoring where silent robotics are necessary.

Fin Ray Stiffness and Fin Morphology Control Ribbon-Fin-Based Propulsion.

Ribbon-fin-based propulsion has rich locomotor capabilities that can enhance the mobility and performance of underwater vehicles navigating in complex environments. Bony fishes using this type of propulsion send one or multiple traveling waves along an elongated fin with the actuation of highly flexible rays that are interconnected by an elastic membrane. In this work, we study how the use of flexible rays and different morphology can affect the performance of ribbon-fin propulsion. We developed a physical model composed of 15 rays that are interconnected with an elastic membrane. We tested four different ray flexural stiffness and four aspect ratios. The robotic model was tested in a low-turbulence flume under two flow conditions ([Formula: see text] wavelength/s). In two experimental sets, we measured fin kinematics, net surge forces, and power consumption. Using these data, we perform a thrust and power analysis of the undulating fin. We present the thrust coefficient, power coefficient, and propulsive efficiency. We find that the thrust generation was linear with the enclosed area swept by the fin, and square of the relative velocity between the incoming flow and traveling wave. The thrust coefficient levels off around 0.5. In addition, for our parameter range, we find that the power consumption scales by the cube of the effective tangential velocity of the rays [Formula: see text] (A is the amplitude of the ray oscillating motion, and [Formula: see text] is the angular velocity). We show that a decay in stiffness decreases both thrust production and power consumption. However, for rays with high flexural stiffness, the difference in thrust compared with rigid rays is minimal. Moreover, our results show that flexible rays can improve the propulsive efficiency compared with a rigid counterpart. Finally, we find that the morphology of ribbon fin affects its propulsive efficiency. For the aspect ratio considered in our experiments, [Formula: see text] was the most efficient compared with [Formula: see text]. Our results suggest that there could be an optimal morphology for a given ribbon fin kinematics. Therefore, both natural swimmers and underwater vehicles using ribbon-fin-based propulsion can take advantage of flexible rays and optimal aspect ratio to improve propulsive performance.

Hydrodynamics of mangrove-type root models: the effect of porosity, spacing ratio and flexibility.

Mangrove trees play a prominent role in coastal tropic and subtropical regions, providing habitats for many organisms and protecting shorelines against high energy flows. In particular, the species Rhizophora mangle (red mangrove) exhibits complex cluster roots interacting with different hydrological flow conditions. To better understand the resilience of mangrove trees, we modeled the roots as a collection of cylinders with a circular pattern subject to unidirectional flow. We investigated the effect of porosity and spacing ratio between roots by varying both the diameter of the patch, D, and inset cylinders, d. In addition, we modeled hanging roots of red mangroves as cantilevered rigid cylinders on a hinge. Force and velocity measurements were performed in a water tunnel (Reynolds numbers from 2200 to 11 000). Concurrently, we performed 2D flow visualization using a flowing soap film. We found that the frequency of the vortex shedding increases as the diameter of the small cylinders decreases while the patch diameter is constant, therefore increasing the Strouhal number, [Formula: see text]. By comparing the change of Strouhal numbers with a single solid cylinder, we introduced a new length scale, the effective diameter. The effective diameter of the patch decreases as the porosity increases. In addition, we found that patch drag scales linearly with the patch diameter but decreases linearly as the spacing ratio increases. After a spacing ratio of ([Formula: see text]), the force scales linearly with the free stream velocity, and the mean velocity behind the patch is independent of the Reynolds number and the patch effect disappears. For flexible cylinders, we found that a decrease in stiffness increases both patch drag and the wake deficit behind the patch in a similar fashion as increasing the blockage of the patch. This information has the potential to help in the development of methods to design resilient bio-inspired coastline structures.

Propulsive performance of an under-actuated robotic ribbon fin.

Many aquatic animals propelled by elongated undulatory fins can perform complex maneuvers and swim with high efficiency at low speeds. In this propulsion, one or multiple waves travel along an elastic fin composed of flexible rays. In this study, we explore the potential benefits or disadvantages of passive fin motion based on the coupling of fluid-structure interactions and elasto-mechanical responses of the undulatory fin. The motivation is to understand how an under-actuated undulating fin can modify its active and passive fin motion to effectively control the hydrodynamic force and propulsive efficiency. We study the kinematics and propulsive performance of an under-actuated ribbon fin using a robotic device. During two experimental sets for fully-actuated fin and under-actuated fin respectively, we measured fin kinematics, surge forces and power consumption. Our results show that under-actuated fin can generate smaller thrust but consume less power comparing to a fully-actuated counterpart. The thrust generated by an under-actuated fin scales similarly to a fully-actuated fin-linear with the enclosed area and quadratic with the relative velocity. Power consumption scales with cube of lateral tangential velocity. Furthermore, we find that the under-actuated fin can keep the same propulsive efficiency as the fully-actuated fin at low relative velocities. This finding has profound implications to both natural swimmers and underwater vehicles using undulating fin-based propulsion, as it suggests that they can potentially exploit passive fin motion without decrementing propulsive efficiency. For underwater vehicles with undulatory fins, an under-actuated design can greatly simplify the mechanical design and control complexity of a versatile propulsion system.

Undulating fins produce off-axis thrust and flow structures.

While wake structures of many forms of swimming and flying are well characterized, the wake generated by a freely swimming undulating fin has not yet been analyzed. These elongated fins allow fish to achieve enhanced agility exemplified by the forward, backward and vertical swimming capabilities of knifefish, and also have potential applications in the design of more maneuverable underwater vehicles. We present the flow structure of an undulating robotic fin model using particle image velocimetry to measure fluid velocity fields in the wake. We supplement the experimental robotic work with high-fidelity computational fluid dynamics, simulating the hydrodynamics of both a virtual fish, whose fin kinematics and fin plus body morphology are measured from a freely swimming knifefish, and a virtual rendering of our robot. Our results indicate that a series of linked vortex tubes is shed off the long edge of the fin as the undulatory wave travels lengthwise along the fin. A jet at an oblique angle to the fin is associated with the successive vortex tubes, propelling the fish forward. The vortex structure bears similarity to the linked vortex ring structure trailing the oscillating caudal fin of a carangiform swimmer, though the vortex rings are distorted because of the undulatory kinematics of the elongated fin.

Biomimetic and bio-inspired robotics in electric fish research.

Weakly electric knifefish have intrigued both biologists and engineers for decades with their unique electrosensory system and agile swimming mechanics. Study of these fish has resulted in models that illuminate the principles behind their electrosensory system and unique swimming abilities. These models have uncovered the mechanisms by which knifefish generate thrust for swimming forward and backward, hovering, and heaving dorsally using a ventral elongated median fin. Engineered active electrosensory models inspired by electric fish allow for close-range sensing in turbid waters where other sensing modalities fail. Artificial electrosense is capable of aiding navigation, detection and discrimination of objects, and mapping the environment, all tasks for which the fish use electrosense extensively. While robotic ribbon fin and artificial electrosense research has been pursued separately to reduce complications that arise when they are combined, electric fish have succeeded in their ecological niche through close coupling of their sensing and mechanical systems. Future integration of electrosense and ribbon fin technology into a knifefish robot should likewise result in a vehicle capable of navigating complex 3D geometries unreachable with current underwater vehicles, as well as provide insights into how to design mobile robots that integrate high bandwidth sensing with highly responsive multidirectional movement.

An aeroelastic instability provides a possible basis for the transition from gliding to flapping flight.

The morphology, kinematics and stiffness properties of lifting surfaces play a key role in the aerodynamic performance of vertebrate flight. These surfaces, as a result of their flexible nature, may move both actively, owing to muscle contraction, and passively, in reaction to fluid forces. However, the nature and implications of this fluid-structure interaction are not well understood. Here, we study passive flight (flight with no active wing actuation) and explore a physical mechanism that leads to the emergence of a natural flapping motion. We model a vertebrate wing with a compliant shoulder and the ability to camber with an idealized physical model consisting of a cantilevered flat plate with a hinged trailing flap. We find that at low wind speed the wing is stationary, but at a critical speed the wing spontaneously flaps. The lift coefficient is significantly enhanced once the wing starts to oscillate, although this increase in lift generation is accompanied by an increase in drag. Flow visualization suggests that a strong leading edge vortex attached to the wing during downstroke is the primary mechanism responsible for the enhanced lift. The flapping instability we observe suggests a possible scenario for an evolutionary transition from gliding to powered flapping flight in animals that possess compliant wings capable of passive camber. Although the flapping state is accompanied by a lower lift-to-drag ratio, the increased lifting capability it confers might have enabled increased body mass, improved foraging performance and/or flight at lower speeds, any of which might have been selectively advantageous.

Kinematics of the ribbon fin in hovering and swimming of the electric ghost knifefish.

Weakly electric knifefish are exceptionally maneuverable swimmers. In prior work, we have shown that they are able to move their entire body omnidirectionally so that they can rapidly reach prey up to several centimeters away. Consequently, in addition to being a focus of efforts to understand the neural basis of sensory signal processing in vertebrates, knifefish are increasingly the subject of biomechanical analysis to understand the coupling of signal acquisition and biomechanics. Here, we focus on a key subset of the knifefish's omnidirectional mechanical abilities: hovering in place, and swimming forward at variable speed. Using high-speed video and a markerless motion capture system to capture fin position, we show that hovering is achieved by generating two traveling waves, one from the caudal edge of the fin and one from the rostral edge, moving toward each other. These two traveling waves overlap at a nodal point near the center of the fin, cancelling fore-aft propulsion. During forward swimming at low velocities, the caudal region of the fin continues to have counter-propagating waves, directly retarding forward movement. The gait transition from hovering to forward swimming is accompanied by a shift in the nodal point toward the caudal end of the fin. While frequency varies significantly to increase speed at low velocities, beyond approximately one body length per second, the frequency stays near 10 Hz, and amplitude modulation becomes more prominent. A coupled central pattern generator model is able to reproduce qualitative features of fin motion and suggest hypotheses regarding the fin's neural control.

Fluid dynamics of the larval zebrafish pectoral fin and the role of fin bending in fluid transport.

Larval zebrafish beat their pectoral fins during many behaviors including low-speed swimming and prey tracking; however, little is known about the functions of these fin movements. Previously, we found experimental support for the function of larval fins in mixing of fluid near the body, which may enhance respiration by diffusion of dissolved oxygen across the skin. Here we use computational fluid dynamics to analyze fluid flow due to the pectoral fin movement. The pectoral fins bend along their proximodistal axis during abduction (fin extension), but remain nearly rigid during adduction (fin flexion). We hypothesize that this asymmetry in bending is critical for fluid mixing near the body and test the effects of fin bending with our simulations. For normal fin beats, we observed similar flow patterns in simulations and experiments. Flow patterns showed fluid stretching and folding, indicative of mixing. When proximodistal bending was removed from fin motion, fins were less effective at transporting fluid in a posterior direction near the body surface, but lateral mixing of fluid near the body was unaffected. Our results suggest that fin bending enhances posterior transport of fluid along the body surface, which may act to aid respiration in combination with lateral stretching and folding of fluid.

Mechanical properties of a bio-inspired robotic knifefish with an undulatory propulsor.

South American electric knifefish are a leading model system within neurobiology. Recent efforts have focused on understanding their biomechanics and relating this to their neural processing strategies. Knifefish swim by means of an undulatory fin that runs most of the length of their body, affixed to the belly. Propelling themselves with this fin enables them to keep their body relatively straight while swimming, enabling straightforward robotic implementation with a rigid hull. In this study, we examined the basic properties of undulatory swimming through use of a robot that was similar in some key respects to the knifefish. As we varied critical fin kinematic variables such as frequency, amplitude, and wavelength of sinusoidal traveling waves, we measured the force generated by the robot when it swam against a stationary sensor, and its velocity while swimming freely within a flow tunnel system. Our results show that there is an optimal operational region in the fin's kinematic parameter space. The optimal actuation parameters found for the robotic knifefish are similar to previously observed parameters for the black ghost knifefish, Apteronotus albifrons. Finally, we used our experimental results to show how the force generated by the robotic fin can be decomposed into thrust and drag terms. Our findings are useful for future bio-inspired underwater vehicles as well as for understanding the mechanics of knifefish swimming.

Aquatic manoeuvering with counter-propagating waves: a novel locomotive strategy.

Many aquatic organisms swim by means of an undulating fin. These undulations often form a single wave travelling from one end of the fin to the other. However, when these aquatic animals are holding station or hovering, there is often a travelling wave from the head to the tail, and another moving from the tail to the head, meeting in the middle of the fin. Our study uses a biomimetic fish robot and computational fluid dynamics on a model of a real fish to uncover the mechanics of these inward counter-propagating waves. In addition, we compare the flow structure and upward force generated by inward counter-propagating waves to standing waves, unidirectional waves, and outward counter-propagating waves (i.e. one wave travelling from the middle of the fin to the head, and another wave travelling from the middle of the fin to the tail). Using digital particle image velocimetry to capture the flow structure around the fish robot, and computational fluid dynamics, we show that inward counter-propagating waves generate a clear mushroom-cloud-like flow structure with an inverted jet. The two streams of fluid set up by the two travelling waves 'collide' together (forming the mushroom cap) and collect into a narrow jet away from the cap (the mushroom stem). The reaction force from this jet acts to push the body in the opposite direction to the jet, perpendicular to the direction of movement provided by a single travelling wave. This downward jet provides a substantial increase in the perpendicular force when compared with the other types of fin actuation. Animals can thereby move upward if the fin is along the bottom midline of the body (or downward if on top); or left-right if the fins are along the lateral margins. In addition to illuminating how a large number of undulatory swimmers can use elongated fins to move in unexpected directions, the phenomenon of counter-propagating waves provides novel motion capabilities for systems using robotic undulators, an emerging technology for propelling underwater vehicles.

The hydrodynamics of ribbon-fin propulsion during impulsive motion.

Weakly electric fish are extraordinarily maneuverable swimmers, able to swim as easily forward as backward and rapidly switch swim direction, among other maneuvers. The primary propulsor of gymnotid electric fish is an elongated ribbon-like anal fin. To understand the mechanical basis of their maneuverability, we examine the hydrodynamics of a non-translating ribbon fin in stationary water using computational fluid dynamics and digital particle image velocimetry (DPIV) of the flow fields around a robotic ribbon fin. Computed forces are compared with drag measurements from towing a cast of the fish and with thrust estimates for measured swim-direction reversals. We idealize the movement of the fin as a traveling sinusoidal wave, and derive scaling relationships for how thrust varies with the wavelength, frequency, amplitude of the traveling wave and fin height. We compare these scaling relationships with prior theoretical work. The primary mechanism of thrust production is the generation of a streamwise central jet and the associated attached vortex rings. Under certain traveling wave regimes, the ribbon fin also generates a heave force, which pushes the body up in the body-fixed frame. In one such regime, we show that as the number of waves along the fin decreases to approximately two-thirds, the heave force surpasses the surge force. This switch from undulatory parallel thrust to oscillatory normal thrust may be important in understanding how the orientation of median fins may vary with fin length and number of waves along them. Our results will be useful for understanding the neural basis of control in the weakly electric knifefish as well as for engineering bio-inspired vehicles with undulatory thrusters.