Body and caudal fin undulations are a widespread locomotion strategy in fish, and their swimming kinematics is usually described by a characteristic frequency and amplitude of the tail-beat oscillation. In some cases, fish use intermittent gaits, where a single frequency is not enough to fully describe their kinematics. Energy efficiency arguments have been invoked in the literature to explain this so-called burst-and-coast regime but well controlled experimental data are scarce. Here we report on an experiment with burst-and-coast swimmers and a numerical model based on the observations to show that: (1) fish modulate a unique intrinsic cycle to sustain the demanded speed by modifying the bursting to coasting ratio while maintaining the duration of the cycle nearly constant; and (2) the chosen kinematics correspond to energy-saving gaits over the range of swimming speeds tested.
Burst-and-coast swimmers optimize gait by adapting unique intrinsic cycle G. Li, I. Ashraf, B. François, D. Kolomenskiy, F. Lechenault, R. Godoy-Diana & B. Thiria Communications Biology 4, 40 (2021) [doi:10.1038/s42003-020-01521-z] preprint: arXiv:2002.09176
We examined experimentally the in-phase and anti-phase synchronized swimming of two self-propelled independent flexible foils swimming side-by-side in a water tank. The foils are actuated by pitching oscillations at one extremity—the head of the swimmers—and the flow engendered by their undulations is analyzed using two-dimensional particle image velocimetry in their frontal symmetry plane. Following recent observations on the behavior of real fish, we focus on the comparison between in-phase and anti-phase actuation by fixing all other geometric and kinematic parameters. We show that swimming with a neighbor is beneficial for both synchronizations tested, as compared to swimming alone, with an advantage for the anti-phase synchronization. We show that the advantage of anti-phase synchronization in terms of swimming performance for the two-foil “school” results from the emergence of a periodic coherent jet between the two swimmers.
See also: On the interference of vorticity and pressure fields of a minimal fish school
G. Li, D. Kolomenskiy, H. Liu, B. Thiria & R. Godoy-Diana Journal of Aero Aqua Bio-mechanisms8 (1), 27-33 (2019) [doi:10.5226/jabmech.8.27]
The physical basis for fish schooling is examined using three-dimensional numerical simulations of a pair of swimming fish, with kinematics and geometry obtained from experimental data. Energy expenditure and efficiency are evaluated using a cost of transport function, while the effect of schooling on the stability of each swimmer is examined by probing the lateral force and the lateral and longitudinal force fluctuations. We construct full maps of the aforementioned quantities as functions of the spatial pattern of the swimming fish pair and show that both energy expenditure and stability can be invoked as possible reasons for the swimming patterns and tail-beat synchronization observed in real fish. Our results suggest that high cost of transport zones should be avoided by the fish. Wake capture may be energetically unfavorable in the absence of kinematic adjustment. We hereby hypothesize that fish may restrain from wake capturing and, instead, adopt side-to-side configuration as a conservative strategy, when the conditions of wake energy harvesting are not satisfied. To maintain a stable school configuration, compromise between propulsive efficiency and stability, as well as between school members, ought to be considered.
Considerable work has been undertaken for the improvement of wave-energy converters and array design. It has recently been suggested that by extracting wave energy, these farms could also serve to protect shorelines from wave damage. The present work focuses on the local effects of wave-structure interactions within an array of oscillating absorbers to optimize global effects, such as reflection, damping, and energy absorption. We use a model system of flexible blades, subjected to monochromatic waves, and develop a simplified one-dimensional model to predict optimal configurations, depending on various parameters, which include the number of blades, their spacing, and their flexibility. Optimal configurations are found to be close to regular patterns, and the impact of array configurations is shown to be limited regarding wave dissipation, mainly due to a competition between reflection and absorption.
Transient locomotion under water is highly constrained by drag and added mass, yet some aquatic snakes catch their prey using a fast forward acceleration, with the mouth opened. These aquatic snakes show a convergence of their head shape in comparison with closely related species that do not forage under water. As both drag and added mass are related to some extent to the shape of the moving object, we explored how shape impacts the hydrodynamic forces applied to the head of a snake during a prey capture event. We compared two 3D- Continue reading “Hydrodynamics of the frontal strike in aquatic snakes”
Image credit: T. Engels (see also Engels et al. Physical Review Fluids 4, 013103, 2019)
Insect and insect-inspired aerodynamics: unsteadiness, structural mechanics and flight control
R. Bomphrey & R. Godoy-Diana Current Opinion in Insect Science30, 26–32 (2018) [doi:10.1016/j.cois.2018.08.003]
Flying insects impress by their versatility and have been a recurrent source of inspiration for engineering devices. A large body of literature has focused on various aspects of insect flight, with an essential part dedicated to the dynamics of flapping wings and their intrinsically unsteady aerodynamic mechanisms. Insect wings flex during flight and a better understanding of structural mechanics and aeroelasticity is emerging. Most recently, insights from solid and fluid mechanics have been integrated with physiological measurements from visual and mechanosensors in the context of flight control in steady airs and through turbulent conditions. We review the key recent advances concerning flight in unsteady environments and how the multi-body mechanics of the insect structure — wings and body — are at the core of the flight control question. The issues herein should be considered when applying bio-informed design principles to robotic flapping wings.
Forced wakes far from threshold: Stuart–Landau equation applied to experimental data
S. Boury, B. Thiria, R. Godoy-Diana, G. Artana, J. E. Wesfreid, and J. D’Adamo Physical Review Fluids3, 091901(R) (2018) [doi:10.1103/PhysRevFluids.3.091901]
We studied with the Stuart-Landau (SL) amplitude equation, a wake flow control scenario using experimental data from a cylinder wake forced by plasma actuators. Given the formal framework recently discussed by Gallaire et al. [Fluid Dyn. Res. 48, 061401 (2016)] on pushing amplitude equations far from threshold, we analyze experimental data of a forced wake in order to test the SL reduced order model. Linear stability theory and global mode concepts are used to determine the SL parameters. The extension to forced wakes of the SL model had been proposed by Thira and Wesfreid [J. Fluid Mech. 579, 137 (2007)] in the context of their study on stability properties, but its employment still remained an open question. Here, we show that a forced wake at a Reynolds number far from the first threshold can also attain the critical behavior described by the SL model.
Surface wave energy absorption by a partially submerged bio-inspired canopy
C. Nové-Josserand, F. Castro Hebrero, L.-M. Petit, W. Megill, R. Godoy-Diana & B. Thiria Bioinspiration & Biomimetics13 036006 (2018) [doi:10.1088/1748-3190/aaae8c]
Aquatic plants are known to protect coastlines and riverbeds from erosion by damping waves and fluid flow. These flexible structures absorb the fluid-borne energy of an incoming fluid by deforming mechanically. In this paper we focus on the mechanisms involved in these fluid-elasticity interactions, as an efficient energy harvesting system, using an experimental canopy model in a wave tank.We study an array of partially-submerged flexible structures that are subjected to the action of a surface wave field, investigating in particular the role of spacing between the elements of the array on the ability of our system to absorb energy from the flow. The energy absorption potential of the canopy model is examined using global wave height measurements for the wave field and local measurements of the elastic energy based on the kinematics of each element of the canopy. We study different canopy arrays and show in particular that flexibility improves wave damping by around 40%, for which half is potentially harvestable.
On the diverse roles of fluid dynamic drag in animal swimming and flying
R. Godoy-Diana & B. Thiria Journal of the Royal Society Interface15 20170715 (2018)
Questions of energy dissipation or friction appear immediately when addressing the problem of a body moving in a fluid. For the most simple problems, involving a constant steady propulsive force on the body, a straightforward relation can be established balancing this driving force with a skin friction or form drag, depending on the Reynolds number and body geometry. This elementary relation closes the full dynamical problem and sets, for instance, average cruising velocity or energy cost. Continue reading “Review paper: Fluid dynamic drag in animal swimming and flying”
Modelling of an actuated elastic swimmer
M. Piñeirua, B. Thiria & R. Godoy-Diana Journal of Fluid Mechanics829 731-750 (2017)
We studied the force production dynamics of undulating elastic plates as a model for fish-like inertial swimmers. Using a beam model coupled with Lighthill’s large-amplitude elongated-body theory, we explore different localised actuations at one extremity of the plate (heaving, pitching and a combination of both) in order to quantify the reactive and resistive contributions to the thrust. The latter has the Continue reading “Flapping elastic plates as a model of fish-like swimmers”
Simple phalanx pattern leads to energy saving in cohesive fish schooling I. Ashraf, H. Bradshaw, T. T. Ha, J. Halloy, R. Godoy-Diana, B. Thiria PNAS114 (36) 9599-9604 (2017) [doi:10.1073/pnas.1706503114]
Synchronisation and collective swimming patterns in Hemigrammus bleheri I. Ashraf, R. Godoy-Diana, J. Halloy, B. Collignon, B. Thiria Journal of the Royal Society Interface1320160734 (2016)
The question of how individuals in a population organize when living in groups arises for systems as different as a swarm of microorganisms or a flock of seagulls. The different patterns for moving collectively involve a wide spectrum of reasons, such as evading predators or optimizing food prospection. Also, the schooling pattern has often been associated with an advantage in terms of energy consumption. We use a popular aquarium fish, the red nose tetra fish, Hemigrammus bleheri, which is known to swim in highly cohesive groups, to ana- lyze the schooling dynamics. In our experiments, fish swim in a shallow-water tunnel with controlled velocity, Continue reading “Synchronisation and pattern formation in fish swimming”
Does aquatic foraging impact head shape evolution in snakes ?
M. Segall, R. Cornette, A-C. Fabre, R. Godoy-Diana & A. Herrel Proceedings of the Royal Society B283 20161645 (2016).
Evolutionary trajectories are often biased by developmental and historical factors. However, environmental factors can also impose constraints on the evolutionary trajectories of organisms leading to convergence of morphology in similar ecological contexts. The physical properties of water impose strong constraints on aquatic feeding animals by generating pressure waves that can alert prey and potentially push them away from the mouth. These hydrodynamic constraints have resulted in the independent evolution of suction feeding in most groups of secondarily aquatic tetrapods. Despite the fact that snakes cannot use suction, they have invaded the aquatic milieu many times independently. Here, we test whether the aquatic environment has constrained head Continue reading “Hydrodynamic constraints and evolution of aquatic snakes”
Resistive thrust production can be as crucial as added mass mechanisms for inertial undulatory swimmers
M. Piñeirua, R. Godoy-Diana & B. Thiria Physical Review E92 021001(R) (2015).
We address here a crucial point regarding the description of moderate to high Reynolds numbers aquatic swimmers. For decades, swimming animals have been classified in two different families of propulsive mechanisms based on the Reynolds number: the resistive swimmers, using local friction to produce the necessary thrust force for locomotion at low Reynolds number, and the reactive swimmers, lying in the high Reynolds range, and using added mass acceleration (described by perfect fluid theory). Continue reading “Resistive thrust production can be as crucial as added mass mechanisms for inertial undulatory swimmers”
Centrifugal instability of Stokes layers in crossflow: the case of a forced cylinder wake
J. D’Adamo, R. Godoy-Diana & J. E. Wesfreid Proceedings of the Royal Society A 471: 20150011 (2015). DOI:10.1098/rspa.2015.0011
A circular cylinder oscillating in a viscous fluid produces an axisymmetric Stokes layer, a fundamental flow susceptible to centrifugal instabilities [see e.g. Seminara & Hall, Proc. Roy. Soc. London A 350, 299 (1976)]. In the present work we study such problem in the wake flow around a circular cylinder at Re = 100 performing rotary oscillations. Continue reading “Centrifugal instability of Stokes layers in crossflow”
Four-winged flapping flyer in forward flight
R. Godoy-Diana, P. Jain, M. Centeno, A. Weinreb & B. Thiria
In Klapp et al. (eds.), Selected Topics of Computational and Experimental Fluid Mechanics, Environmental Science and Engineering, pp. 147-158. Springer (2015).
We study experimentally a four-winged flapping flyer with chord-wise flexible wings in a self-propelled setup. For a given physical configuration of the flyer (i.e. fixed distance between the forewing and hindwing pairs and fixed wing flexibility), we explore the kinematic parameter space constituted by the flapping frequency and the forewing-hindwing phase lag. Continue reading “Four-winged flapping flyer in forward flight”
We study experimentally the propulsive dynamics of flexible undulating foils in a self-propelled swimming configuration near a wall. Measurements of swimming speed and propulsive force are performed, together with full recordings of the elastic wave kinematics and particle image velocimetry. Continue reading “Undulatory swimming near a wall”
Vortex-induced drag and the role of aspect ratio in undulatory swimmers
V. Raspa, S. Ramananarivo, B. Thiria & R. Godoy-Diana. Physics of Fluids, 26 : 041701 (2014).
During cruising, the thrust produced by a self-propelled swimmer is balanced by a global drag force. For a given object shape, this drag can involve skin friction or form drag, both being well-documented mechanisms. However, for swimmers whose shape is changing in time, the question of drag is not yet clearly established. Continue reading “Drag in undulatory swimmers”
Propagating waves in bounded elastic media: an application to the efficiency of bio-inspired swimmers
S. Ramananarivo, R. Godoy-Diana & B. Thiria. EPL, 105 : 54003 (2014).
Confined geometries usually involve reflected waves interacting together to form a spatially stationary pattern. Our recent study on the locomotion of a self-propelled elastic swimmer on a free surface [Ramananarivo et al. 2013], however, has shown that propagating wave kinematics can naturally emerge in a forced elastic rod, even with boundary conditions involving significant reflections. This particular behavior is observed only in the presence of strong damping. Continue reading “Propagating waves in bounded elastic media”
Passive elastic mechanism to mimic fish-muscles action in anguilliform swimming
S. Ramananarivo; R. Godoy-Diana & B. Thiria. Journal of the Royal Society Interface10 : 20130667 (2013).
Abstract: Swimmers in nature use body undulations to generate propulsive and maneuvering forces. The an- guilliform kinematics is driven by muscular actions all along the body, involving a complex temporal and spatial coordination of all the local actuations. Such swimming kinematics can be reproduced artificially, in a simpler way, by using passively the elasticity of the body. Here we present experiments on self-propelled elastic swimmers at a free surface in the inertial regime. Continue reading “Passive elastic mechanism to mimic fish-muscles action in anguilliform swimming”
Topology-induced effect in biomimetic propulsive wakes
V. Raspa; R. Godoy-Diana & B. Thiria. Journal of Fluid Mechanics, 729: 377-387 (2013).
Abstract: It is known that the wake pattern observed in a cross-section behind swimming or flying animals is typically characterized by the presence of periodical vortex shedding. However, depending on species, propulsive wakes can differ according to the spatial ordering of the main vortex structures. We conducted a very precise experiment to analyse the role of the topology of the wake in the generation of propulsion by comparing two prototypical cases in a quasi-two-dimensional view. Continue reading “Topology-induced effect in biomimetic propulsive wakes”
Force balance in the take-off of a pierid butterfly: relative importance and timing of leg impulsion and aerodynamic forces
G. Bimbard, D. Kolomenskiy, O. Bouteleux, J. Casas & R. Godoy-Diana. Journal of Experimental Biology, 216 : 3551-3563 (2013).
Abstract: Up to now, the take-off stage remains an elusive phase of insect flight relatively poorly explored compared to other maneuvers. An overall assessment of the different mechanisms involved in the force production during take-off has never been explored. Focusing on the first downstroke, we have addressed this problem from a force balance perspective in butterflies taking-off from the ground. Continue reading “Force balance in the take-off of a pierid butterfly”
Spatiotemporal spectral analysis of a forced cylinder wake
J. D’Adamo; R. Godoy-Diana & J. E. Wesfreid. Physical Review E, 84 : 056308 (2011).
Abstract: The wake of a circular cylinder performing rotary oscillations is studied using hydrodynamic tunnel experiments at $Re=100$. Two-dimensional particle image velocimetry on the mid-plane perpendicular to the axis of cylinder is used to characterize the spatial development of the flow and its stability properties. Continue reading “Spatiotemporal spectral analysis of a forced cylinder wake”
Rather than resonance, flapping wing flyers may play on aerodynamics to improve performance
S. Ramananarivo; R. Godoy-Diana & B. Thiria. Proceedings of the National Academy of Sciences (USA), 108 (15): 5964-5969 (2011).
Abstract: Saving energy and enhancing performance are secular preoccupations shared by both nature and human beings. In animal locomotion, flapping flyers or swimmers rely on the flexibility of their wings or body to passively increase their efficiency using an appropriate cycle of storing and releasing elastic energy. Despite the convergence of many observations pointing out this feature, the underlying mechanisms explaining how the elastic nature of the wings is related to propulsive efficiency remain unclear. Here we use an experiment with a self-propelled simplified insect model allowing to show how wing compliance governs the performance of flapping flyers. Continue reading “Behind the performance of flapping wing flyers”
Convective instability in inhomogeneous media: impulse response in the subcritical cylinder wake
C. Marais; R. Godoy-Diana; D. Barkley & J. E. Wesfreid. Physics of Fluids, 23 (1): 014104 (2011).
Abstract: We study experimentally the impulse response of a cylinder wake below the critical Reynolds number of the Bénard-von Kármán instability. In this subcritical regime, a localized inhomogeneous region of convective instability exists which causes initial perturbations to be transiently amplified. The aim of this work is to quantify the evolution resulting from this convective instability using two-dimensional particle image velocimetry in a hydrodynamic tunnel experiment. Continue reading “Impulse response in the subcritical cylinder wake”
Abstract: Wing flexibility governs the flying performance of flapping-wing flyers. Here, we use a self-propelled flapping-wing model mounted on a ”merry go roun” to investigate the effect of wing compliance on the propulsive efficiency of the system. Continue reading “Bending to fly”
A model for the symmetry breaking of the reverse Bénard-von Kármán vortex street produced by a flapping foil
R. Godoy-Diana; C. Marais; J. L. Aider & J. E. Wesfreid. Journal of Fluid Mechanics, 622 : 23-32 (2009).
Abstract: The vortex streets produced by a flapping foil of span-to-chord aspect ratio of 4:1 are studied in a hydrodynamic tunnel experiment. In particular, the mechanisms giving rise to the symmetry breaking of the reverse Bénard-von Kármán vortex street that characterizes fish-like swimming and forward flapping flight are examined. Two-dimensional particle image velocimetry measurements in the mid-plane perpendicular to the span axis of the foil are used to characterize the different flow regimes. Continue reading “Symmetry breaking of the reverse Bénard-von Kármán vortex street”
Transitions in the wake of a flapping foil
R. Godoy-Diana; J. L. Aider & J. E. Wesfreid. Physical Review E, 77 : 016308 (2008).
Abstract: We study experimentally the vortex streets produced by a flapping foil in a hydrodynamic tunnel, using two-dimensional particle image velocimetry. An analysis in terms of a flapping frequency-amplitude phase space allows the identification of (i) the transition from the well-known Bénard-von Kármán (BvK) wake to the reverse BvK vortex street that characterizes propulsive wakes, and (ii) the symmetry breaking of this reverse BvK pattern giving rise to an asymmetric wake. Continue reading “Transitions in the wake of a flapping foil”
On the tuning of a wave-energy driven oscillating-water-column seawater pump to polychromatic waves
R. Godoy-Diana & S. P. R. Czitrom. Ocean Engineering, 34 : 2374-2384 (2007).
Abstract: Performance of wave-energy devices of the oscillating water column (OWC) type is greatly enhanced when a resonant condition with the forcing waves is maintained. The natural frequency of such systems can in general be tuned to resonate with a given wave forcing frequency. In this paper we address the tuning of an OWC sea-water pump to polychromatic waves. We report results of wave tank experiments, which were conducted with a scale model of the pump. Continue reading “Tuning a wave-energy-driven OWC seawater pump to polychromatic waves”
Internal gravity waves in a dipolar wind: a wave–vortex interaction experiment in a stratified fluid
R. Godoy-Diana; J. M. Chomaz & C. Donnadieu. Journal of Fluid Mechanics, 548 : 281-308 (2006).
Abstract: An experimental study on the interaction of the internal wave field generated by oscillating cylinders in a stratified fluid with a pancake dipole is presented. The experiments are carried out in a salt-stratified water tank with constant Brunt–Väisälä frequency ($N$). Experimental observations of the deformation of the wave beams owing to the interaction with the dipole are presented. Continue reading “Internal gravity waves in a dipolar wind”
Effect of the Schmidt number on the diffusion of axisymmetric pancake vortices in a stratified fluid
R. Godoy-Diana & J. M. Chomaz. Physics of Fluids, 15 : 1058-1064 (2003).
Abstract: An asymptotic analysis of the equations for quasi-two-dimensional flow in stratified fluids is conducted, leading to a model for the diffusion of pancake-like vortices in cyclostrophic balance. This analysis permits one to derive formally the model for the diffusion of an axisymmetric monopole proposed by Beckers et al. [J. Fluid Mech. 433, 1 (2001)], and to extend their results. The appropriate parameter for the perturbation analysis is identified as the square of the vertical Froude number Fv=U/(Lv N), where U is the horizontal velocity scale, N is the Brunt–Väisälä frequency, and Lv the vertical length scale. Continue reading “Diffusion of pancake-like vortices in cyclostrophic balance”
Hydrodynamics of an oscillating water column seawater pump. Part I: Theoretical Aspects
S. P. R. Czitrom; R. Godoy; E. Prado; P. Pérez & R. Peralta-Fabi. Ocean Engineering, 27 : 1181-1198 (2000).
Abstract: A wave-driven seawater pump, composed of a resonant and an exhaust duct joined by a variable-volume air compression chamber, is studied. The time dependent form of Bernoulli’s equation, adapted to incorporate losses due to friction, vortex formation at the mouths and radiation damping, describes the pump behaviour. A dimensional analysis of the pump equations shows that a proposed scale-model will perform similar to a full-scale seawater pump. Continue reading “Hydrodynamics of an oscillating water column seawater pump”
Hydrodynamics of an oscillating water column seawater pump. Part II: Tuning to Monochromatic Waves
S. P. R. Czitrom; R. Godoy; E. Prado; A. Olvera & C. Stern. Ocean Engineering, 27 : 1199-1219 (2000).
Abstract: Flume experiments with a scale-model of a wave driven seawater pump in monochromatic waves are described. A tuning mechanism optimises the pump performance by keeping it at resonance with the waves. The pumping process itself was found to de-tune the system because of the reduced gravity restoring force due to spilling in the compression chamber. A perturbation analysis of the pump equations shows that performance of the system can be increased by optimising the shape of the pump intake to minimise losses due to vortex formation. Continue reading “Hydrodynamics of an oscillating water column seawater pump (Part II)”
Vortex suppresion in an oscillating flow
C. Stern; S. Czitrom; E. Prado & R. Godoy. Revista Mexicana de Fisica, 46 : 409-410 (2000).
Abstract: The motivation for this work was the reduction of losses due to vortex formation at the entrance of a wave driven seawater pump. Measurements in a wave tank using a prototype had shown a 10% ¡ncrease in the pumping efficiency when a trumpet like shape was added to the intake. This lead us to search for an inlake that would reduce or completely suppress vortex formation. In this experiment a piston produces an oscil1ating flow inside a partly submerged duct. At the end of the duct four different shapes were tested. Continue reading “Vortex suppresion in an oscillating flow”
Oscillating Flow through a Funnel
C. Stern; S. Czitrom & R. Godoy. Physics of Fluids, 11 : S3 (Gallery of Fluids) (1999).
Abstract: Our interest in vortex suppression at the entrance of a wave-driven seawater pump leads us to study vortex formation at the exit of a diffuser due to an oscillating flow. In the present experiment, a piston produces an oscillating flow inside a partly submerged duct that ends in a diffuser. The diffuser is designed such that a constant relationship between centripetal and inertial forces is maintained along the profile. The flow in the near field of the mouth is visualized by injecting diluted fluorescent water paint just outside the diffuser. Continue reading “Oscillating Flow through a Funnel”