While swimming in their natural environment, marine organisms must successfully forage, escape from predation, and search for mates to reproduce. In the process, planktonic organisms interact with their fluid environment, generating fluid signatures around their body and in their downstream wake through ontogeny. In the early stages of their life cycle, marine organisms operate in environments where viscous effects dominate and govern physical processes. Ontogenetic propulsive transitions in swimming organisms often involve dramatic changes in morphology and swimming behavior. However, for organisms that do not undergo significant changes in morphology, swimming behavior or propulsive mode, how is their swimming performance affected? We investigated the ontogenetic propulsive transitions of the hydromedusa Sarsia tubulosa, which utilizes jet propulsion and possesses a similar bell morphology throughout its life cycle. We used digital particle image velocimetry and high-speed imaging to measure the body kinematics, velocity fields and wake structures induced by swimming S. tubulosa with bell exit diameters from 1 to 10 mm. Our experimental observations revealed three distinct classes of hydrodynamic wakes: elongated vortex rings for 10<Re<30 (1–2 mm bell exit diameter), classical elliptical vortex rings for Re>30 (larger than 2 mm bell exit diameter) and elliptical vortex rings (or leading vortex rings) followed by trailing jets for most instances where Re>100 (larger than 4 or 5 mm bell exit diameter). The relative travel distance and propulsive efficiency remained unchanged throughout ontogeny, and the swimming proficiency and hydrodynamic cost of transport decreased non-linearly.
The fitness of marine planktonic organisms depends on their ability to successfully undertake a variety of processes (i.e. forage, search for mates to reproduce, and escape from predation) in their fluid environment (Visser, 2007). While undergoing these activities, organisms generate fluid signatures around their body and in their downstream wake, and the presence of these wakes can directly affect the organism's fitness (Videler et al., 2002; Dickinson, 2003; Visser, 2007). In the early stages of their life cycle, marine organisms operate in environments where viscous effects are significant and govern physical processes (Kiørboe and Visser, 1999; Catton et al., 2011). As organisms grow and develop through ontogeny, individuals experience their fluid environment differently as they transition from viscous-dominated fluid regimes to inertially dominated regimes (Bartol et al., 2008). In order to overcome the changing role of viscosity in their environment, organisms may employ different strategies, biomechanics and behaviors. Ontogeny studies provide information about these strategies and behaviors as marine organisms interact with their fluid environment.
Swimming organisms utilize many different strategies to travel from one location to the next, which include (but are not limited to) ciliary modes, paddling and jet propulsion (Vogel, 2008). Ciliary propulsion tends to dominate flows where viscous effects far exceed inertial effects and Reynolds numbers (Re) are up to 100 (Childress and Dudley, 2004; Humphries, 2013). Jetting and paddling propulsion are swimming strategies that are more prevalent in intermediary and high Reynolds number regimes (Vogel, 2008; Herschlag and Miller, 2011). Jet propulsion is widespread in biology, and is utilized by many different organisms, including squid (Johnson et al., 1972; Wells and O'Dor, 1991; Anderson and Grosenbaugh, 2005; Bartol et al., 2008), salps (Bone and Trueman, 1983; Madin, 1990; Sutherland and Madin, 2010) and medusae (Daniel, 1983; DeMont and Gosline, 1988; Dabiri et al., 2006). Jet propulsion often involves fast contraction of muscles to create an impulsive jet in the form of a vortex ring (Daniel, 1983; Vogel, 2008). In squid, mantle contraction and expulsion of fluid through a smaller diameter funnel creates strong vortex rings (Johnson et al., 1972; Wells and O'Dor, 1991; Bartol et al., 2008). In medusae, circumferential muscles contract and expel fluid from the subumbrellar cavity to create vortex rings (Daniel, 1983; DeMont and Gosline, 1988; Dabiri et al., 2006).
Free-swimming medusae utilize two conserved swimming modes: rowing and jet propulsion (Colin and Costello, 2002; Costello et al., 2008). For both swimming modes, contraction of the bell by subumbrellar muscles expels fluid from the subumbrellar cavity and creates a starting vortex (Dabiri et al., 2005). During relaxation of the same subumbrellar muscles, fluid is brought into the subumbrellar cavity as a result of a drop in internal pressure, and creates a stopping vortex (Dabiri et al., 2005; Sahin et al., 2009). Rowing propulsion is characterized by strong interactions between these stopping and starting vortices to achieve a propulsive advantage (Dabiri et al., 2005). In contrast, jet propulsion seems to lack this interaction (Weston et al., 2009; Sahin et al., 2009). Based on the medusan morphospace, propulsive mode is largely determined by the fineness ratio, or the ratio between the height and width of the bell (Costello et al., 2008). For medusae with small fineness ratio (oblate body planforms), rowing propulsive mode is observed. For medusae with large fineness ratios (prolate body planforms), jetting propulsive mode is observed (Costello et al., 2008). Interestingly, these swimming modes are strongly linked to behavior with trade-offs for energetics and performance (Ford and Costello, 2000; Costello et al., 2008; Dabiri et al., 2010). Rowing medusae tend to feed and swim constantly, while jetting medusae are often ambush predators, consuming prey that contact tentacles during long, motionless periods (Colin and Costello, 2002; Colin et al., 2003). As rowing propulsion is more efficient (higher useful work compared with total work) than jetting, and jetting is more proficient (higher peak velocities compared with bell diameter) than rowing, the duration of swimming maximizes feeding rates and minimizes energy expenditure for both rowing and jetting medusae (Colin and Costello, 2002; Colin et al., 2003; Dabiri et al., 2010).
amplitude of swimming stroke
coefficient of drag
total cost of transport
distance traveled during a single swimming cycle
bell exit diameter
digital particle image velocimetry
force due to drag
force due to thrust
hydrodynamic cost of transport
maximum fluid impulse
fluid kinetic energy
maximum fluid kinetic energy
jellyfish body mass
radial distance from the axis of rotation
duration of bell contraction
duration of total swimming cycle
bell thickness at apex
maximum swimming speed
volume in space
velocity field grid mesh spacing
Froude or propulsive efficiency
Froude or propulsive efficiency based on drag
Froude or propulsive efficiency based on thrust
fluid kinematic viscosity
Medusae utilize different strategies to swim and forage through ontogeny (Ford and Costello, 2000; McHenry and Jed, 2003; Weston et al., 2009; Feitl et al., 2009; Blough et al., 2011). Juvenile leptomedusae, Aequorea victoria and Eutonina indicans, have bells with high fineness ratio (prolate morphology), and after reaching 4 or 5 mm in bell diameter, transition to bells with low fineness ratios (oblate morphology; Weston et al., 2009). Changes in bell morphology are often accompanied by changes in swimming mode and behavior: juvenile leptomedusae utilize jet propulsion and rarely swim; adults utilize rowing propulsion and swim continuously (Weston et al., 2009). Studies of jet propulsion in squid through ontogeny have also revealed differences in swimming mode and behavior. The propulsive wakes and resulting energetics of adult Lolliguncula brevis and Doryteuthis pealeii paralarvae showed that squid paralarvae rely almost entirely on jet propulsion for swimming, and adult squid rely on fins more often (Bartol et al., 2008, 2009a,b). The propulsive efficiency for squid paralarvae was higher than for the adult forms (Bartol et al., 2009a). However, fins were observed to be more active during swimming of adult squid, which may improve propulsive efficiency (Bartol et al., 2008, 2009a). Therefore, adult squid and squid paralarvae together cannot be used as a model animal for investigating how effective jet propulsion is for an organism that has similar morphology and swimming mode throughout ontogeny.
For organisms going through development in the transitional Reynolds number regime (Re from 100 to 102), it is desirable for them to maintain a similar propulsive efficiency and relative travel distance throughout ontogeny (Taylor et al., 2003). This may be due to constraints set by a variety of factors that include (but are not limited to) growth demands, encounter rates and predator–prey interactions. Organisms have at least two ways to achieve this: (1) by modifying morphology (including propulsive morphology) and swimming mode/behavior, or (2) by maintaining the same morphological features but modifying swimming kinematics. In other words, for organisms that do not undergo significant changes in morphology and propulsive mode through ontogeny, what swimming strategies are employed to overcome relative changes in their fluid environment?
Here, we investigated the propulsive transitions over ontogeny of the hydromedusa Sarsia tubulosa (M. Sars 1835), which utilizes the same swimming mode (jet propulsion) throughout its life cycle (Colin et al., 2003). In addition, S. tubulosa does not undergo significant changes in bell morphology through ontogeny (Edwards, 1978). Therefore, we can investigate swimming kinematics and energetics of S. tubulosa to understand how a solely jet-propelled organism is able to overcome the effects of fluid viscosity, and transition to fluid regimes where both inertial and viscous effects are important to fluid processes. For S. tubulosa, and many other species of medusae, size is an indicator of developmental stage (Weston et al., 2009; Blough et al., 2011). In this study, we used body size of S. tubulosa as a proxy for ontogenetic life stage. We used digital particle image velocimetry (DPIV) and high speed imaging to measure the body kinematics, velocity fields and wake structures induced by swimming S. tubulosa ranging in size from 1 to 10 mm bell exit diameter. Using the kinematic data and velocity field data, the propulsive efficiency, swimming proficiency and hydrodynamic cost of transport (HCOT) can be evaluated over ontogeny, and a relationship between these quantities and the hydrodynamic wakes generated during swimming can be explored.
Using the methods described below, kinematic and energetic parameters can be quantified to compare swimming ability and biomechanics of S. tubulosa across ontogeny. With size scale (specifically bell exit diameter) as a proxy for ontogenetic life stage, scaling laws can be derived for quantities that include maximum swimming speed, distance traveled, swimming proficiency, propulsive efficiency and HCOT, which can be used to elucidate ecomechanical consequences of growth in aquatic biological systems.
Kinematics parameters through ontogeny
As bell exit diameter of S. tubulosa increased, the total swimming cycle duration increased linearly (R2=0.84, P<0.001), and the relaxation duration increased at a faster rate than the contraction duration (Fig. 1; kinematics across size scales are shown in supplementary material Movie 1). The relaxation duration was always longer than the contraction duration over the entire range of bell exit diameters. The coast duration changed with bell exit diameter (R2=0.47, P<0.001); however, there were instances where no coasting phase was observed. Differences in bell kinematics and size resulted in differences in swimming speed (Fig. 2). The normalized bell exit diameter (the ratio between time-varying bell exit diameter and maximum bell exit diameter; Fig. 2A) and normalized swimming speed (the ratio between time-varying swimming speed and maximum swimming speed; Fig. 2B) varied with normalized time (time divided by total swimming cycle time). As bell exit diameter increased, the contraction phase duration increased (also shown in Fig. 1). The normalized swimming speed for S. tubulosa with 1 mm exit diameter decayed rapidly compared with the larger size classes. For S. tubulosa with 9 mm exit diameter, the maximum swimming speed nearly coincided with the end of the contraction phase. For the smaller size classes, the maximum swimming speed was reached approximately 0.09 s prior to the end of the contraction phase, which constituted 23% of the contraction phase duration.
Average values for contraction time (tc), distance traveled per swimming cycle (d) and maximum swimming speed (Umax) are shown for each size class in Table 1. A comparison of all individuals revealed that as bell exit diameter increased, the distance traveled increased linearly (R2=0.80), whereas the maximum swimming speed increased as a power law (R2=0.60; Fig. 3B). However, this increasing trend was reversed when the swimming speed was normalized by animal size (or bell exit diameter, De; Fig. 3D). As bell exit diameter increased, the swimming proficiency (p) decreased to the power of −0.63 (R2=0.88). The relative distance traveled (travel distance normalized by bell exit diameter; Fig. 3C) had substantial variability with increasing bell exit diameter, and a linear regression (not shown) was found to be not significant (R2=0.04, P>0.05).
Dimensionless parameters, such as Reynolds number Re and Strouhal number St, provide details on whether the swimming kinematics of S. tubulosa has dynamic similarity across ontogeny. Compiling all collected data revealed a statistically significant linear relationship between bell exit diameter and Re (R2=0.96, P<0.001; Fig. 4). The minimum and maximum Re were 13 and 300, respectively, which corresponded to S. tubulosa with a 1 mm and a 10.5 mm bell exit diameter. This Reynolds number range extended from fluid regimes where viscous forces are significant to intermediary ranges where inertial effects become more important to hydrodynamic processes. Strouhal number remained bounded between 0.1 and 0.3 (Fig. 5; gray dashed lines), with a mean and standard deviation of 0.20±0.07 (Fig. 5; black dashed line) through development. A linear regression of St varying with bell exit diameter De (not shown) was not statistically significant (R2=0.03, P>0.05).
Hydrodynamic wakes and energetics parameters through ontogeny
Velocity and vorticity fields revealed differences in the hydrodynamic signatures surrounding the body and in the wake of S. tubulosa (Fig. 6; velocity fields of three different size scales are shown in supplementary material Movie 2). Smearing of the vorticity field due to viscosity resulted in an elongated starting vortex structure in the wake of S. tubulosa with a bell exit diameter of 1 mm. For S. tubulosa with bell exit diameters of 2 mm and larger, the vortex ring transitioned to a classical elliptical shape. As bell exit diameter increased from 4 to 6 mm, the starting vortex structure transitioned from a classical elliptical vortex ring to an elliptical vortex ring with a trailing jet. However, not all S. tubulosa with a bell exit diameter greater than 5 mm generated a trailing jet, thereby indicating that organisms at this size scale have the ability to exhibit swimming modes with and without a trailing jet. Of the data sets where bell exit diameter exceeded 4 mm (20 data sets), 15 events where trailing jets emerged in the hydrodynamic wake were measured.
The maximum specific fluid kinetic energy (i.e. the maximum fluid kinetic energy divided by the fluid density, KEmax/ρ) and the maximum specific fluid impulse (Imax/ρ) in the propulsive wake of S. tubulosa revealed the changing energetics through ontogeny of S. tubulosa (Fig. 7). As bell exit diameter increased, KEmax/ρ and Imax/ρ increased as a power law of 3.23 and 1.89, respectively (R2>0.90, P<0.001 for both). Using the values of Imax, KEmax and Umax (see Table 1 for average values by size class), the propulsive efficiency (ηF; see Materials and methods, Eqn 6) across size scales can be determined (Fig. 8). Linear trend lines (not shown) for either formulation of propulsive efficiency were not statistically significant (R2 values of 0.007 and 0.004 for ηFD and ηFT, respectively; P>0.05 for both). Finally, the HCOT decreased with increasing body exit diameter and body mass (m) (Fig. 9). Power law trend lines for both bell exit diameter and body mass had R2 values greater than 0.65 and were statistically significant (P<0.001).
We observed swimming by S. tubulosa up ontogeny starting at 1 mm bell exit diameter up to 10 mm. The Reynolds number range experienced through ontogeny (Fig. 4) started at approximately 10 and reached upwards of 300. Throughout ontogeny, S. tubulosa were able to achieve jet propulsion and vortex formation during both the contraction and relaxation phases (Fig. 6). However, the characteristics of the wake structures generated by swimming S. tubulosa changed through ontogeny. These changes in kinematics and hydrodynamics yielded a reduction in swimming proficiency (i.e. body length s−1) and a non-increasing trend in propulsive efficiency with bell exit diameter. We showed that S. tubulosa modifies its swimming kinematics over ontogeny to maintain high propulsive efficiency, which was supported by the narrow Strouhal number range (Fig. 5). This extensive data set is the first to compare the hydrodynamic structures generated by swimming medusae that do not exhibit any substantial changes in morphology or swimming behavior throughout development.
Jetting medusae: experimental versus numerical models
The smallest size scales of free-swimming S. tubulosa corresponded to 1 mm bell exit diameters with Reynolds numbers of 10. This size scale was above the apparent lower limit for jet propulsion at Re=5 (Herschlag and Miller, 2011) and the theoretical limit for vortex ring formation (Cantwell, 1986). The total swimming cycle of S. tubulosa was composed of a contraction phase, a coasting period and then a relaxation phase. The contraction and relaxation durations for the smallest size scales were remarkably similar, with a non-zero coasting phase in between (Fig. 1). As bell exit diameter increased, the total swimming duration increased linearly, and the contraction duration increased more slowly than the relaxation time. The numerical models of Herschlag and Miller (2011) compared the hydrodynamic wakes generated by simulated prolate medusae by maintaining swimming kinematics (where tc=2.43 s and time of relaxation tr=3tc) through ontogeny and varying Re. The measured contraction phase durations through ontogeny (Fig. 1 and Table 1) were nearly an order of magnitude smaller than those used by Herschlag and Miller (2011). Although true kinematics would significantly improve model results, their observations will nonetheless contribute to our discussion here.
The distance traveled over a single swimming cycle increased linearly with increasing bell exit diameter (Fig. 3A). The travel distances reported here were measured after one swimming cycle starting from rest, and the relative travel distance was approximately two bell exit diameters through ontogeny (Fig. 3C). After four consecutive swimming cycles, prolate medusae (Re>32) were predicted to travel between five and eight body lengths after starting from rest (Herschlag and Miller, 2011). Despite differences in swimming kinematics and behavior, the observed and predicted relative travel distances are in good agreement. Additionally, the measured maximum swimming speed of S. tubulosa began to level off at bell exit diameters larger than 4 or 5 mm (Fig. 3B). The same trend was observed in the prolate model, where for Re greater than 100, the average forward velocity began to plateau (Herschlag and Miller, 2011). This power law trend in swimming speed resulted in swimming proficiency decreasing over ontogeny (Fig. 3D) by roughly 60% between 1 mm and 4 or 5 mm bell exit diameters.
Jet propulsion by S. tubulosa was observed through ontogeny, with a starting and stopping vortex generated during the contraction and relaxation phases, respectively (Fig. 6). Our observations differed from those of Weston et al. (2009), where no stopping vortex was observed during the relaxation phase of 2 mm Aequorea victoria, a prolate jetting medusae. We suspect that differences in our observations arose from the visualization technique, where the presence of coherent vortex structures relies on the available amount of dye to illuminate the stopping vortex. The generation of a stopping vortex during relaxation was predicted by all numerical and model studies of swimming by prolate adult medusae and through ontogeny (Sahin et al., 2009; Lipinski and Mohseni, 2009; Herschlag and Miller, 2011). Some numerical results suggest that the presence of the velum traps the stopping vortex within the subumbrellar cavity (Lipinski and Mohseni, 2009). The visualization method used in this study did not reveal velum motion for organisms at all size ranges, so we cannot comment on whether the velum retained the stopping vortex. The numerical results of Herschlag and Miller (2011), which did not consider velum kinematics, found that in all Re cases, the stopping vortex traveled up into the subumbrellar cavity. We observed that a stopping vortex was generated during bell relaxation, and under its own translational velocity, the stopping vortex remained in the subumbrellar cavity of S. tubulosa until it dissipated. As Re increased, the presence of the stopping vortex was enhanced and persisted longer than at smaller size scales, where viscous diffusion plays a larger role (Herschlag and Miller, 2011).
Our experimental observations revealed three distinct classes of hydrodynamic wakes: elongated vortex rings for 10<Re<30 (1–2 mm bell exit diameter), classical elliptical vortex rings for Re>30 (larger than 2 mm bell exit diameter) and, in most instances where Re>100 (larger than 4 or 5 mm bell exit diameter), elliptical vortex rings (or leading vortex rings) followed by trailing jets (Fig. 6). Of the numerical studies considered here, none showed hydrodynamic wake structures besides elliptical vortex rings (Sahin et al., 2009; Lipinski and Mohseni, 2009; Herschlag and Miller, 2011). Elongated vortex rings have been observed in wakes created by impulsively jumping copepods and jetting paralarvae (Jiang and Kiørboe, 2011a,b; Bartol et al., 2008, 2009a,b), whose power stroke (or contraction time) durations are 5–100 ms, an order of magnitude less than those prescribed by Herschlag and Miller (2011). In two numerical studies of swimming by adult S. tubulosa, realistic kinematics based on experimental data were prescribed (Sahin et al., 2009; Lipinski and Mohseni, 2009), and the formation time of the wake vortex ring was found to be greater than the universal value of 4 (Gharib et al., 1998). It is believed that the time variable change in the velar diameter and the acceleration of fluid from the subumbrellar cavity acted to prevent the emergence of a trailing jet (Mohseni and Gharib, 1998; Sahin et al., 2009), which is consistent with other observations of formation time by jetting medusae (Dabiri et al., 2006). Although the characterization of vortex formation was not included here, we suspect that the emergence of the trailing jet corresponds to hydrodynamic wakes with vortex formation times larger than 8.
Jet propulsion by medusae and squid through ontogeny
The ontogenetic propulsive transitions by juvenile and adult brief squid L. brevis and D. pealeii paralarvae (Bartol et al., 2008, 2009a,b) are similar to those observed in S. tubulosa. Squid paralarvae rely heavily on jet propulsion and do not employ their fins until adult stages (Bartol et al., 2008, 2009a,b). Elongated vortex rings formed in the propulsive wakes of D. pealeii paralarvae for individuals with dorsal mantle lengths of approximately 0.18 cm. As squid grew in size between 3 and 9 cm dorsal mantle lengths, elliptical vortex rings and trailing jets emerged (Bartol et al., 2008, 2009a). For the larger sized L. brevis, two jet modes were identified, where jet mode I consisted of a leading vortex and jet mode II consisted of a leading vortex and trailing jet. Interestingly, the authors found that squid with dorsal mantle lengths less than 5 cm utilized jet mode I greater than jet mode II (Bartol et al., 2009a). The utilization of jet mode I over jet mode II for smaller size scales is consistent with findings for S. tubulosa, where medusae in the Reynolds number range 30<Re<100 used jet mode I (leading, elliptical vortex ring only), and for Re>100 (4–5 mm bell exit diameter), jet modes I and II were employed.
The propulsive efficiency of squid jet propulsion over ontogeny decreased with increasing squid mantle length (Bartol et al., 2008). Paralarvae had significantly higher jet propulsive efficiencies than juveniles or adults, with a measured range of 73.5–95.8% and 49.4–88.8%, respectively (Bartol et al., 2008). As squid grew, fin use increased, and when fin propulsion was considered with the jet, overall propulsive efficiency increased with increasing dorsal mantle length (Bartol et al., 2009a). Therefore, the ontogenetic trend in propulsive efficiency for jetting squid may not be clear as the use of fins may reduce the dependence on jet propulsion for adult squid. Using the same formulation for propulsive efficiency based on the thrust produced in the jet wake (ηFT; Fig. 8), we did not see a significant decreasing trend with bell exit diameter in S. tubulosa. To be sure, propulsive efficiency (based on the drag produced during swimming, ηFD) of jetting medusae utilizing jet mode II is less than that of similarly sized rowing medusae generating propulsive wakes similar to jet mode I (Dabiri et al., 2010). If all adult S. tubulosa utilized jet mode II, we would see a stronger decreasing trend in propulsive efficiency over ontogeny (Fig. 8).
Interestingly, ontogenetic studies of squid and medusae have shown that these organisms are able to exhibit different swimming modes and generate different hydrodynamic wakes through ontogeny, with selection for some swimming modes in a specific Reynolds number range. In this study, we showed that elongated vortex rings were utilized in S. tubulosa where Re<30 (1–2 mm bell exit diameters), and classical elliptical vortex rings were solely exhibited between 30>Re>100 (2–4 mm bell exit diameters). Beyond Reynolds numbers of 100 (>4 or 5 mm bell exit diameters), adult S. tubulosa swim by generating elliptical vortex rings (jet mode I) and leading vortex rings with trailing jets (jet mode II). Instead of transitioning from jet mode I to jet mode II at 4 or 5 mm bell exit diameters, some leptomedusae (Aequorea victoria and Eutonina indicans) transition to large, oblate, rowing medusae at the same size range (Weston et al., 2009). This transition in morphology and swimming mode was also accompanied by changes in behavior, with A. victoria and E. indicans swimming nearly continuously as adult rowing medusae. The reasons for this rapid transition from a jetting medusa to a rowing medusa at 4 or 5 mm bell diameter in A. victoria and E. indicans may be related to this transition between jet mode I and jet mode II, where jet mode II is energetically less efficient (Dabiri et al., 2010).
HCOT over ontogeny
The HCOT, unlike the total cost of transport (COT), relies on the quantification of energy invested during jetting to estimate the total energy (including the metabolic investment) expended during locomotion. Although the HCOT provides only a minimum estimate of metabolic economy, we expect that the behavior of HCOT across ontogeny will reflect the COT. Metabolic rates for other medusae utilizing rowing propulsion have been collected for Aurelia aurita, Stomolophus meleagris and Stomotoca atra (Uye and Shimauchi, 2005; Larson, 1987; Daniel, 1985). Although respiration rates have been quantified for similarly sized Gonionemus vertens (Daniel, 1985), metabolic rates across ontogeny for jet-propelled medusae have yet to be measured. Therefore, the use of HCOT as a proxy for COT is warranted.
The HCOT for S. tubulosa ranged from 0.01 to 10 J kg−1 m−1 for body masses from 10−4 to 1 g (Fig. 9B). Although these values were higher than those reported for S. meleagris (Larson, 1987), the results here represent size ranges smaller than those reported for S. meleagris. For organisms with a body mass of 0.01 g, the values of HCOT for S. tubulosa were consistent with COT values for S. atra and G. vertens (Daniel, 1985). The high rates of acceleration and deceleration during jet propulsion could explain higher values of HCOT compared with S. meleagris, a rowing-propelled medusa (Daniel, 1985). When plotted on a log–log plot (Fig. 9B), the HCOT of S. tubulosa became non-linear for a range of body masses beyond 0.03 and 0.04 g, corresponding to organisms with bell exit diameters of 5 mm (Table 1). The maximum swimming speed over ontogeny for S. tubulosa was also non-linear; after a linear increase for the smallest bell exit diameters, the maximum swimming speed reached a constant (approximately 4 cm s−1) for bell exit diameters larger than 5 mm. Non-linearity of COT (on log–log plots) and maximum swimming speed has been reported for S. meleagris, and was attributed to insufficiently powerful muscle mass in larger organisms (Larson, 1987).
In addition to insufficient muscular power, the change in behavior of HCOT and swimming speed may be related to differences in hydrodynamic wake structures, where the generation of a leading vortex and trailing jet was observed for S. tubulosa with bell exit diameters larger than 5 mm (Fig. 6). In the case of S. meleagris and other rowing-propelled medusae, we do not expect to see a trailing jet for larger size scales (Costello et al., 2008; Dabiri et al., 2010). Therefore, asymptotic behavior of swimming speed in S. meleagris may solely be a result of muscle mass limitations. In the case of S. tubulosa and other jet-propelled medusae, hydrodynamic costs combined with insufficiently powerful muscle mass limits the body size of jet-propelled medusae (Costello et al., 2008). These ideas may apply to jet-propelled swimmers more generally, where jet propulsion is used as a sole swimming mechanism for smaller organisms, and jet propulsion is used sparingly or in conjunction with other swimming modes or mechanisms in larger swimmers (e.g. medusae and squid; Colin et al., 2003; Bartol et al., 2008).
MATERIALS AND METHODS
Measurements of swimming S. tubulosa began in spring of 2006 and ended in spring of 2012, and were conducted at the Marine Biological Laboratory (MBL) and Woods Hole Oceanographic Institution (WHOI; autumn of 2010, spring and autumn of 2011) in Woods Hole, MA, USA, and Friday Harbor Laboratory (FHL; spring of 2006 and 2012) in Friday Harbor, WA, USA. The smallest organisms, with 1–4 mm bell exit diameters, were acquired as newly budded medusae from cultures of S. tubulosa polyps (temperature at 10°C and salinity of 35 psu, density (ρ) and viscosity (ν) correspond to 1026.95 kg m−3 and 1.354×10−6 m2 s−1, respectively). Larger medusae, of 3–10 mm bell exit diameter, were hand collected from the field in both Woods Hole and Friday Harbor. All medusae were maintained in chilled seawater (10°C and 35 psu).
We used body size scale (specifically, bell exit diameter) as a proxy for ontogenetic life stage in cultured and collected organisms. The swimming behavior and fluid interactions of all medusae were analyzed using variably sized rectangular glass filming vessels of dimensions that were sufficiently large (dimensions much greater than 20 times the medusan diameters) to avoid wall effects. For all measurements, 10 µm glass beads were added to the filming vessel for seeding visualization. The seawater temperature was carefully maintained at 10–12°C throughout the analyses.
In spring of 2006 (at FHL), data sets were collected where organisms swam through the plane of a 1 mm thick laser sheet produced by a 250 mW, 532 nm continuous laser (Wicked Lasers, China). The particle motion induced by swimming S. tubulosa was recorded at 30 frames s–1 onto a digital video tape via a 720×480 pixel CCD array (Sony HDR-FDX1, Sony Electronics Inc., USA) resulting in a viewing area of 70 cm2. In spring of 2012, a high-speed camera (Fastcam SA3, Photron Inc., Japan) and lens (Nikon Inc., Japan) resulted in viewing areas of approximately 25 cm2. Illumination was achieved by cylindrical optics and a 1 W, 671 nm, red laser (LaVision Inc., Germany), creating a 1 mm thick light sheet. Swimming and resulting flow fields were captured at 1000 frames s–1 at 1024×1024 pixel resolution.
In Woods Hole, animal swimming motions were captured using a high-speed camera (Fastcam SA3, Photron Inc.), a variety of prime lenses (100, 60, 50 and 35 mm; Carl Zeiss Inc., Germany and Nikon Inc., Japan), and extension tubes to yield viewing areas from 1 to 16 cm2. Illumination was provided by a 300 W, 808 nm, near-infrared laser (Firefly, Oxford Lasers, UK), and built-in optics generated a light sheet 0.5 mm thick. In order to resolve high-speed, short duration flows generated by S. tubulosa, images were captured at 1000 frames s−1 at full, 1024×1024 pixel resolution. Data sets where the body (indicated by the laser sheet intersecting the manubrium) and propulsive wake were bisected by the laser sheet within the camera's field of view before, during and after the swimming cycle were used for subsequent analysis. Of the 133 data sets collected, results from 67 data sets are presented here.
The wet body mass (m) was estimated from the video images, where the tissue thickness (T) at the bell apex and the maximum diameter of the medusa bell (D) were measured prior to the start of contraction. Assuming that the animal was neutrally buoyant in seawater, the body tissues should have the same density as seawater (ρ=1026.95 kg m−3). The medusan body shape was approximated by a hemiellipsoid, with height characterized by thickness T at the apex (and zero thickness at the mid-point) and width characterized by maximum bell diameter D. Therefore, the mass of the medusan body can be estimated by .
Velocity fields were calculated with DaVis (LaVision Inc., Germany), a DPIV (Adrian, 1991; Willert and Gharib, 1991) software package, using a multi-pass algorithm. For the lower resolution images (720×480 pixels) collected in spring of 2006, the initial and final interrogation window sizes were 132×132 pixels and 64×64 pixels. For higher resolution images (1024×1024 pixels), the initial and final interrogation window sizes were 64×64 pixels and 32×32 pixels, respectively. For both image resolutions, the overlap between interrogation windows was 50%. Velocity field data were exported from DaVis and additional post-processing steps were conducted using an in-house Matlab processing code.
The authors gratefully acknowledge the assistance provided by J. O. Dabiri and E. Klos during field work and animal collections conducted at the Friday Harbor Laboratories (University of Washington) in 2006. We would also like to thank B. J. Gemmell for his assistance with organisms cultured at Marine Biological Laboratories in Woods Hole, MA.
K.K., H.J., S.P.C. and J.H.C. designed and conceived this study. K.K., S.P.C. and J.H.C. collected the data used in this study. K.K. analyzed the data, interpreted the findings and prepared the manuscript. K.K., H.J., S.P.C. and J.H.C. revised the submission.
This work was supported by the National Science Foundation [IOS-1353937 and OCE-1433979 to H.J., OCE-1061353 to J.H.C. and OCE-1242229 to S.P.C.] and Woods Hole Oceanographic Institution's Office of Research [Ocean Life Institute grant to H.J., Devonshire Foundation grant to K.K.]. K.K. is supported by the Postdoctoral Fellow Program at the Monterey Bay Aquarium Research Institute and the Marine Life Observatory at Hopkins Marine Station (Stanford University).
The authors declare no competing or financial interests.