'Optimal' vortex rings and aquatic propulsion mechanisms

Fishes swim by flapping their tail and other fins. Other sea creatures, such as squid and salps, eject fluid intermittently as a jet. We discuss the fluid mechanics behind these propulsion mechanisms and show that these animals produce optimal vortex rings, which give the maximum thrust for a given energy input. We show that fishes optimize both their steady swimming efficiency and their ability to accelerate and turn by producing an individual optimal ring with each flap of the tail or fin. Salps produce vortex rings directly by ejecting a volume of fluid through a rear orifice, and these are also optimal. An important implication of this paper is that the repetition of vortex production is not necessary for an individual vortex to have the 'optimal' characteristics.     

A Prototype of a Biomimetic Mantle Jet Propeller Inspired by Cuttlefish Actuated by SMA Wires and a Theoretical Model for Its Jet Thrust

The cuttlefish have higher swimming speed and more maneuverability than most of the fish mainly benefiting from their unique jet propulsion mechanism, which is realized by the contraction and expansion of their flexible mantle. However it is difficult to mimic this jet propulsion mechanism using conventional electro-mechanical structures. In this paper, the musculature of the cuttlefish mantle and how the mantle flexibly contracts and expands were analyzed first. Then the Shape Memory Alloy（SMA） wires were chosen as the actuators and the soft silica gel was chosen as the body materials to develop a biomimetic mantle jet propeller. The SMA wires were embedded within the soft silica gel formed with cuttlefish mantle shape along the annular direction to mimic the circular muscles of cuttlefish mantle. The water was squeezed out the mantle cavity to form rear jets when the biomimetic mantle was contracted by SMA wires. A mechanical model and a thermal model were established to analyze the jet thrust and the jetting frequency. Theoretical analysis shows that the jet thrust is proportional to the square of the rate of change of SMA strain. Increasing the driving voltage can improve the rate of change of SMA strain, thus can improve both the jet thrust and the jetting frequency. However the j etting frequency is mainly restricted by the cooling of SMA wires. To maximize the jetting frequency, the optimal driving parameters for different driving voltage were calculated. The propulsion performance was tested and the results show that the jet thrust can increase with the driving voltage as predicted and the maximum average jet thrust is 0.14 N when the driving voltage is 25 V. The swimming test was carried out to verify the feasibility of the novel design. It is shown that the biomimetic jet propeller can swim with higher speed as the jet thrust and jetting frequency increase and the maximum speed can reach 8.76 cm·s^-1 （0.35 BL·s^-1） at a jetting frequency of 0.83 Hz.     

Jet propulsion in Doliolum (Tunicata: Thaliacea)

The jet propulsion of doliolid gonozooids is described from a combination of kinematic, chamber pressure, and muscle electrical records. Doliolids respond to light mechanical stimuli by a rapid contraction of the locomotor muscle bands, producing a single jet pulse which drives the animal forwards or backwards at instantaneous velocities up to 21.4cm·s^?1 (over 50 body lengths·s^?1). Spike potentials from the (multiply innervated) locomotor muscle fibres are variable in size and probably are non-propagating. Maximum chamber pressures during the jet pulse range up to 500 Pa, doliolids ≈4.5 mm long perform around 4 × 10^?6 J work per contraction. Although the locomotor system is specialized for single rapid escape movements, the same movements are used at irregular intervals to maintain the horizontal position of the animal (which is denser than sea water) in the water column. The locomotor system is less economical than that of salps.     

Ontogeny of squid mantle function: changes in the mechanics of escape-jet locomotion in the oval squid,Sepioteuthis lessoniana lesson, 1830

In Sepioteuthis lessoniana, the oval squid, ontogenetic changes in the kinematics of the mantle during escape-jet locomotion imply a decline in the relative mass flux of the escape jet and may affect the peak weight-specific thrust of the escape jet. To examine the relationship between ontogenetic changes in the kinematics of the mantle and the thrust generated during the escape jet, we simultaneously measured the peak thrust and the kinematics of the mantle of squid tethered to a force transducer. We tested an ontogenetic series of S. lessoniana that ranged in size from 5 to 40 mm dorsal mantle length (DML). In newly hatched squids, thrust peaked 40 ms after the start of the escape jet and reached a maximum of between 0.10 mN and 0.80 mN. In the largest animals, thrust peaked 70 ms after the start of the escape jet and reached a maximum of between 18 mN and 110 mN. Peak thrust was normalized by the wet weight of the squid and also by the cross-sectional area of the circumferential muscle that provides power for the escape jet. The weight-specific peak thrust of the escape jet averaged 0.36 in newly hatched squid and increased significantly to an average of 1.5 in the largest squids measured (P < 0.01). The thrust per unit area of circumferential muscle averaged 0.25 mN/mm(2) in hatchlings and increased significantly to an average of 1.4 mN/mm(2) in the largest animals tested (P < 0.01). The impulse of the escape jet was also lowest in newly hatched individuals (1.3 mN. s) and increased significantly to 1000 mN. s in the largest squids measured (P < 0.01). These ontogenetic changes in the mechanics of the escape jet suggest (1) that propulsion efficiency of the exhalant phase of the jet is highest in hatchlings, and (2) that the mechanics of the circumferential muscles of the mantle change during growth.     

The locomotory function of the fins in the squid Loligo pealei

Kinematic data of high spatial and temporal resolution, acquired from image sequences of adult long-finned squid, Loligo pealei, during steady swimming in a flume, were used to examine the role of fins and the coordination between fin and jet propulsion in squid locomotion. Fin shape and body outlines were digitized and used to calculate fin wave speed, amplitude, frequency, angle of attack, body deformation, speed, and acceleration. L. pealei were observed to have two fin gait patterns with a transition at 1.4-1.8 mantle lengths per second (Lm s-1) marked by alternation between the two patterns. Fin motion in L. pealei exhibited characteristics of both traveling waves and flapping wings. At low speeds, fin motion was more wave-like; at high speeds, fin motion was more flap-like and was marked by regular periods during which the fins were wrapped tightly against the mantle. Fin cycle frequencies were dependent on swimming speed and gait, and obvious coordination between the fins and jet were observed. Fin wave speed, angle of attack, and body acceleration confirmed the role of fins in thrust production and revealed a role of fins at all swimming speeds by a transition from drag-based to lift-based thrust when fin wave speed dropped below swimming speed. Estimates of peak fin thrust were as high as 0.44-0.96 times peak jet thrust in steady swimming over the range of swimming speeds observed. Fin downstrokes generally contributed more to thrust than did upstrokes, especially at high speeds.     

The locomotory function of the fins in the squid Loligo pealei

Kinematic data of high spatial and temporal resolution, acquired from image sequences of adult long-finned squid, Loligo pealei, during steady swimming in a flume, were used to examine the role of fins and the coordination between fin and jet propulsion in squid locomotion. Fin shape and body outlines were digitized and used to calculate fin wave speed, amplitude, frequency, angle of attack, body deformation, speed, and acceleration. L. pealei were observed to have two fin gait patterns with a transition at 1.4-1.8 mantle lengths per second (L_m s^-1) marked by alternation between the two patterns. Fin motion in L. pealei exhibited characteristics of both traveling waves and flapping wings. At low speeds, fin motion was more wave-like; at high speeds, fin motion was more flap-like and was marked by regular periods during which the fins were wrapped tightly against the mantle. Fin cycle frequencies were dependent on swimming speed and gait, and obvious coordination between the fins and jet were observed. Fin wave speed, angle of attack, and body acceleration confirmed the role of fins in thrust production and revealed a role of fins at all swimming speeds by a transition from drag-based to lift-based thrust when fin wave speed dropped below swimming speed. Estimates of peak fin thrust were as high as 0.44-0.96 times peak jet thrust in steady swimming over the range of swimming speeds observed. Fin downstrokes generally contributed more to thrust than did upstrokes, especially at high speeds.     

Power requirements of swimming: do new methods resolve old questions?

A recurring question in the study of fish biomechanics and energeticsis the mechanical power required for tail-swimming at the highspeeds seen among aquatic vertebrates. The quest for answershas been driven by conceptual advances in fluid dynamics, startingwith ideas on the boundary layer and drag initiated by Prandtl,and in measurement techniques starting with force balances focussingon drag and thrust. Drag (=thrust) from measurements on physicalmodels, carcasses, kinematics as inputs to hydromechanical models,and physiological power sources vary from less than that expectedfor an equivalent rigid reference to over an order of magnitudegreater. Estimates of drag and thrust using recent advanceslargely made possible by increased computing power have notresolved the discrepancy. Sources of drag and thrust are notseparable in axial undulatory self propulsion, are open to interpretationand Froude efficiency is zero. Wakes are not easily interpreted,especially for thrust evaluation. We suggest the best measuresof swimming performance are velocity and power consumption forwhich 2D inviscid simulations can give realistic predictions.Steady swimming power is several times that required for towingan equivalent flat plate at the same speed.     

Propulsion in Cubomedusae: Mechanisms and Utility

Evolutionary constraints which limit the forces produced during bell contractions of medusae affect the overall medusan morphospace such that jet propulsion is limited to only small medusae. Cubomedusae, which often possess large prolate bells and are thought to swim via jet propulsion, appear to violate the theoretical constraints which determine the medusan morphospace. To examine propulsion by cubomedusae, we quantified size related changes in wake dynamics, bell shape, swimming and turning kinematics of two species of cubomedusae, Chironex fleckeri and Chiropsella bronzie. During growth, these cubomedusae transitioned from using jet propulsion at smaller sizes to a rowing-jetting hybrid mode of propulsion at larger sizes. Simple modifications in the flexibility and kinematics of their velarium appeared to be sufficient to alter their propulsive mode. Turning occurs during both bell contraction and expansion and is achieved by generating asymmetric vortex structures during both stages of the swimming cycle. Swimming characteristics were considered in conjunction with the unique foraging strategy used by cubomedusae.     

Biologically-Inspired Water Propulsion System

Most propulsion systems of vehicles travelling in the aquatic environment are equipped with propellers. Observations of nature, however, show that the absolute majority of organisms travel through water using wave motion, paddling or using water jet power. Inspired by these observations of nature, an innovative propulsion system working in aquatic environment was developed. This paper presents the design of the water propulsion system. Particular attention was paid to the use of paddling techniques and water jet power. A group of organisms that use those mechanisms to travel through water was selected and analysed. The results of research were used in the design of a propulsion system modelled simultaneously on two methods of movement in the aquatic environment. A method for modelling a propulsion system using a combination of the two solutions and the result were described. A conceptual design and a prototype constructed based on the solution were presented. With respect to the solution developed, studies and analyses of selected parameters of the prototype were described.     

The effect of Reynolds number on the propulsive efficiency of a biomorphic pulsed-jet underwater vehicle

The effect of Reynolds number on the propulsive efficiency of pulsed-jet propulsion was studied experimentally on a self-propelled, pulsed-jet underwater vehicle, dubbed Robosquid due to the similarity of its propulsion system with squid. Robosquid was tested for jet slug length-to-diameter ratios (L/D) in the range 2-6 and dimensionless frequency (St(L)) in the range 0.2-0.6 in a glycerin-water mixture. Digital particle image velocimetry was used for measuring the impulse and energy of jet pulses from the velocity and vorticity fields of the jet flow to calculate the pulsed-jet propulsive efficiency, and compare it with an equivalent steady jet system. Robosquid's Reynolds number (Re) based on average vehicle velocity and vehicle diameter ranged between 37 and 60. The current results for propulsive efficiency were compared to the previously published results in water where Re ranged between 1300 and 2700. The results showed that the average propulsive efficiency decreased by 26% as the average Re decreased from 2000 to 50 while the ratio of pulsed-jet to steady jet efficiency (η(P)/η(P, ss)) increased up to 0.15 (26%) as the Re decreased over the same range and for similar pulsing conditions. The improved η(P)/η(P, ss) at lower Re suggests that pulsed-jet propulsion can be used as an efficient propulsion system for millimeter-scale propulsion applications. The Re = 37-60 conditions in the present investigation, showed a reduced dependence of η(P) and η(P)/η(P, ss)on L/D compared to higher Re results. This may be due to the lack of clearly observed vortex ring pinch-off as L/D increased for this Re regime.     

Transitions from Drag-based to Lift-based Propulsion in Mammalian Swimming

The evolution of fully aquatic mammals from quadrupedal, terrestrialmammals was associated with changes in morphology and swimmingmode. Drag is minimized by streamlining body shape and appendages.Improvement in speed, thrust production and efficiency is accomplishedby a change of swimming mode. Terrestrial and semiaquatic mammalsemploy drag-based propulsion with paddling appendages, whereasfully aquatic mammals use lift-based propulsion with oscillatinghydrofoils. Aerobic efficiencies are low for drag-based swimming,but reach a maximum of 30% for lift-based propulsion. Propulsiveefficiency is over 80% for lift-based swimming while only 33%for paddling. In addition to swimming mode, the transition tohigh performance propulsion was associated with a shift fromsurface to submerged swimming providing a reduction in transportcosts. The evolution of aquatic mammals from terrestrial ancestorsrequired increased swimming performance with minimal compromiseto terrestrial movement. Examination of modern analogs to transitionalswimming stages suggests that only slight modification to theneuromotor pattern used for terrestrial locomotion is requiredto allow for a change to lift-based propulsion.     

Braking Performance of a Biomimetic Squid-Like Underwater Robot

In this study, the braking performance of the undulating fin propulsion system of a biomimetic squid-like underwater robot was investigated through free run experiment and simulation of the quasi-steady mathematical model. The quasi-steady equations of motion were solved using the measured and calculated hydrodynamic forces and compared with free-run test results. Various braking strategies were tested and discussed in terms of stopping ability and the forces acting on the stopping stage. The stopping performance of the undulating fin propulsion system turned out to be excellent considering the short stopping time and short stopping distance. This is because of the large negative thrust produced by progressive wave in opposite direction. It was confirmed that the undulating fin propulsion system can effectively perform braking even in complex underwater explorations.     

Reynolds number limits for jet propulsion: a numerical study of simplified jellyfish

The Scallop theorem states that reciprocal methods of locomotion, such as jet propulsion or paddling, will not work in Stokes flow (Reynolds number=0). In nature the effective limit of jet propulsion is still in the range where inertial forces are significant. It appears that almost all animals that use jet propulsion swim at Reynolds numbers (Re) of about 5 or more. Juvenile squid and octopods hatch from the egg already swimming in this inertial regime. Juvenile jellyfish, or ephyrae, break off from polyps swimming at Re greater than 5. Many other organisms, such as scallops, rarely swim at Re less than 100. The limitations of jet propulsion at intermediate Re is explored here using the immersed boundary method to solve the 2D Navier-Stokes equations coupled to the motion of a simplified jellyfish. The contraction and expansion kinematics are prescribed, but the forward and backward swimming motions of the idealized jellyfish are emergent properties determined by the resulting fluid dynamics. Simulations are performed for both an oblate bell shape using a paddling mode of swimming and a prolate bell shape using jet propulsion. Average forward velocities and work put into the system are calculated for Re between 1 and 320. The results show that forward velocities rapidly decay with decreasing Re for all bell shapes when Re<10. Similarly, the work required to generate the pulsing motion increases significantly for Re<10. When compared to actual organisms, the swimming velocities and vortex separation patterns for the model prolate agree with those observed in Nemopsis bachei. The forward swimming velocities of the model oblate jellyfish after two pulse cycles are comparable to those reported for Aurelia aurita, but discrepancies are observed in the vortex dynamics between when the 2D model oblate jellyfish and the organism. This discrepancy is likely due to a combination of the differences between the 3D reality of the jellyfish and the 2D simplification, as well as the rigidity of the time varying geometry imposed by the idealized model.     

A general law for animal locomotion?

The propulsion system of animals that fly or swim are quite different from each other in their morphology and function, yet the propulsive efficiency could be maximized by a surprising similarity in the fine tuning of flapping frequency, amplitude and forward speed, according to a new study by Taylor et al. This conclusion was based on an analysis of the Strouhal number, which is a dynamic similarity index relevant to propulsion that relies on vortex shedding for thrust generation. Such fine-tuning of the propulsive system suggests possible consequences for physiological and ecological adaptations related to, for example muscle operating frequency and optimal speed of muscle contraction.     

A biomimetic robotic jellyfish (Robojelly) actuated by shape memory alloy composite actuators

An analysis is conducted on the design, fabrication and performance of an underwater vehicle mimicking the propulsion mechanism and physical appearance of a medusa (jellyfish). The robotic jellyfish called Robojelly mimics the morphology and kinematics of the Aurelia aurita species. Robojelly actuates using bio-inspired shape memory alloy composite actuators. A systematic fabrication technique was developed to replicate the essential structural features of A. aurita. Robojelly's body was fabricated from RTV silicone having a total mass of 242 g and bell diameter of 164 mm. Robojelly was able to generate enough thrust in static water conditions to propel itself and achieve a proficiency of 0.19 s(-1) while the A. aurita achieves a proficiency of around 0.25 s(-1). A thrust analysis based on empirical measurements for a natural jellyfish was used to compare the performance of the different robotic configurations. The configuration with best performance was a Robojelly with segmented bell and a passive flap structure. Robojelly was found to consume an average power on the order of 17 W with the actuators not having fully reached a thermal steady state.     

Experimental and Numerical Study of Penguin Mode Flapping Foil Propulsion System for Ships

The use of biomimetic tandem flapping foils for ships and underwater vehicles is considered as a unique and interesting concept in the area of marine propulsion.The flapping wings can be used as a thrust producing,stabilizer and control devices which has both propulsion and maneuvering applications for marine vehicles.In the present study,the hydrodynamic performance of a pair of flexible flapping foils resembling penguin flippers is studied.A ship model of 3 m in length is fitted with a pair of counter flapping foils at its bottom mid-ship region.Model tests are carried out in a towing tank to estimate the propulsive performance of flapping foils in bollard and self propulsion modes.The same tests are performed in a numerical environment using a Computational Fluid Dynamics (CFD) software.The numerical and experimental results show reasonably good agreement in both bollard pull and self propulsion trials.The numerical studies are carried out on flexible flapping hydrofoil in unsteady conditions using moving unstructured grids.The efficiency and force coefficients of the flexible flapping foils are determined and presented as a function of Strouhal number.     

Distribution of salps near the South Shetland Islands during austral summer, 1990–1991 with special reference to krill distribution

Distribution and biomass of salps and Antarctic krill (Euphausia superba) were investigated near the South Shetland Islands during austral summer 1990–1991. Salp biomass ranged between 0 and 556 mgC·m^–3 and was greatest at a station in the Bransfield Strait in late December 1990. Salp biomass was lower than that of E. superba. Two species of salps; Salpa thompsoni and Ihlea racovitzai were found, and the former was dominant numerically. Spatial distribution and generation composition of these two species was different. Spatial distributions of salps and E. superba did not overlap particularly so the January–February period. While E. superba was found mainly in the coastal area which showed high-chlorophyll a values, salps exhibited high biomass in the oceanic area with low chlorophyll a concentrations. Predation by salps on small krill and the competitive removal of food by them, are discussed as potential reasons for the relatively low abundance of E. superba at the stations where salps were present in great numbers.     

Ammonite aptychi: Functions and role in propulsion

Seven previous proposals of aptychus (sensu stricto) function are reviewed: lower mandible, protection of gonads of females, protective operculum, ballasting, flushing benthic prey, filtering microfauna and pump for jet propulsion. An eighth is introduced: aptychi functioned to actively stabilize the rocking produced by the pulsating jet during forward foraging and backward swimming. Experiments with in-air models suggest that planispiral ammonites could lower their aperture by the forward shift of a mobile cephalic complex. In the experiments, the ventral part of the peristome is lowered from the lateral resting (neutral) position by the added “ballast” of a relatively thin Laevaptychus to an angle < 25° from horizontal with adequate stability to withstand the counter-force produced by the jet of the recurved hyponome. However, of the shell forms tested, only brevidomes with thick aptychi, e.g., the Upper Jurassic Aspidoceratidae with Laevaptychus and average whorl expansion rates, were stable enough to swim forward by jet propulsion at about Nautilus speed (∼ 25 cm/s). We propose that aptychus function most commonly combined feeding (jaw, flushing, filtering) with protection (operculum), and, more rarely, with locomotion (ballast, pump, diving and stabilizing plane). Aptychi may thus have been multi-functional.     

Zooplankton feeding ecology: clearance and ingestion rates of the salps Thalia democratica, Cyclosalpa affinis and Salpa cylindrica on naturally occurring particles in the Mid-Atlantic Bight

Aggregate stages of the salps Thalia democratica, Cyclosalpaaffinis and Salpa cylindrica collected by SCUBA diving in theMid-Atlantic Bight were fed with naturally occurring food assemblages.This is one of the few studies where salps have been fed withnatural food assemblages. The estimated clearance rate for allspecies based on disappearance of chlorophyll varied from 82to 444 mL individual^–1 day^–1. Cell counts showedthat T. democratica mostly ingested carbon from autotrophicnanoflagellates and autotrophic dinoflagellates. Ingestion byS. cylindrica was primarily on larger prey, such as dinoflagellates,while C. affinis ingested auto- and heterotrophic nanoflagellates.All main prey types ingested by salps corresponded to thosethat contributed most to biomass at each experimental station.Thus, salps fed on naturally occurring particles primarily inproportion to prey biomass and to their mechanical capacityto be retained and ingested. Feeding by salps on dinoflagellatesand ciliates implies that they may act not only as potentialcompetitors with microzooplankton, but also as consumers ofthem.     

Antarctic krill (Euphausia superba Dana) eat salps

 Feeding behaviour of Antarctic krill (Euphausia superba) on salps was observed in shipboard experiments during the 1994/1995 Kaiyo Maru Antarctic Ocean research cruise. The feeding rate was more than 0.5 salp/krill per day. When offered ethanol extracts of four prey types, salps, phytoplankton, krill and polychaetes, krill preferred the salp extracts. This evidence implies that the substances extracted from salps were most attractive to krill. These results might indicate a tight ecological relationship between krill and salps. Received: 24 May 1995/Accepted: 8 October 1995