Introduction

             Unlike the air that we are familiar with, ocean water is far more viscous, making it more difficult to move about. Marine animals can be benthic, spending most of their time on the floor of the ocean, or pelagic, spending most of their time within the water column. They can be found swimming in the wide open, barren deep sea or within crowded coral reefs in shallow water. There are thousands of marine animals with a wide variety of body forms and swimming forms because they reside in different habitats within the ocean.  The five swimming forms that will be discussed include jet propulsion, drag powered, hydrofoil, body-caudal fin, and median paired fin propulsion. 

Jet Powered Swimming

            The body of a jellyfish is shaped like a parachute, which is known as the bell. The sides of jellyfish consist of an extracellular ‘jelly’ that is lined with a layer of enveloping tissue. This tissue layer consists of individual muscle cells aligned in a singular sheet. For a jellyfish to move, it must contract these muscle cells to send a wave of motion down the bell. The force of this jet propulsion motion is correlated to the thickness of the muscle, with larger muscle creating more force.  To trade mass for motion as in jet engines, the extremely flexible bell engulfs water taken in from outside of the bell to gain momentum. As water is forced out of the bell during muscle contraction, the jellyfish is thrusted forward. Then, as the bell expands again and fills with water, this movement slows down and the process repeats. This can be observed in the Japanese sea nettle (Chrysaora melanaster) as exemplified Video 1 quite well. The advantage of having an elastic bell is to increase the speed at which fluid exits the aperture, increasing the thrust action. The size of the parachute on a jellyfish determines the rate at which these contractions occur or pulsate, with smaller parachutes pulsating more rapidly than larger medusas for equal propulsion speeds (Colin et al., 2013). 

           Fluids are by definition mostly incompressible. This implies that as the area of a jellyfish's aperture decreases from muscle contraction within the bell, the rate at which water is being expelled increases. This is known as the law of continuity: the velocity of the fluid exiting a conduit such as aperture of a jellyfish is inversely proportional to the cross section of the opening. For example, if the diameter of the aperture is doubled, then the velocity of the water expelled is reduced by half. As force is defined as the product of a given mass and the acceleration rate of that mass, the force created by jet propulsion can be calculated by multiplying the mass of the water expelled and its acceleration. Jellyfish that have evolved a larger bell thus display lower thrusts than their smaller contemporaries by contracting more slowly. This forms a flatter bell that contains less water and wider openings into the bell. When jellyfish contract their bells, two vortices of water or eddies are formed behind them. In jellyfish propulsion, these eddies are close enough together to destructively interfere and thus cancel each other out. This lowers the force of drag behind the bell that opposes forward motion, allowing jellyfish to thrust forward more efficiently (McHenry, 2007). 

             

                 Video 1: Japanese sea nettle (Chrysaora melanaster)

            Jellyfish can be broken up into two groups based on the shape of their bell: oblate and prolate. Oblate jellyfish have flatter bells, such as Lion's mane jelly (Cyanea capillata) seen in Video 3. Prolate jellyfish, such as the White-spotted jelly (Phyllorhiza punctata) in Video 2,  have more rounded bells. The rate at which the bell contracts is faster in prolate jellyfish than oblate jellyfish. Accordingly, this means that prolate jellyfish swim faster than oblate jellyfish. Swimming performance is maximized in jellyfish when bell contraction produces the fastest thrust with the lowest force of resistance against the water. Rapid bell contractions with a limited area in which water can escape from the aperture increase the momentum of the jet propulsion. From a dynamic viewpoint, the prominent forces acting in jet propulsion include drag, acceleration, and the amount of force needed to overcome inertia. Streamlined body forms decrease the amount of energy expended, increasing swimming efficiency and performance. Maximum acceleration occurs immediately after large pulses of the bell. As a way to measure how efficiently aquatic animals swim through water, the Reynolds number is physical ratio commonly applied in the study of fluid dynamics. The Reynolds number is defined as the  dimensionless quotient of intrinsic inertial and extrinsic viscous forces acting on a body in a fluid. Thus, a jellyfish swimming with a high Reynolds number is experiencing low viscous drag and resistance from the water with a high degree of force applied to move through the water. The Reynolds number is often correlated with the acceleration rates of jellyfish and is the largest after a bell contraction and at the beginning of bell relaxation (Colin & Costello, 2002). 

Video 2: White-spotted jelly (Phyllorhiza punctata)

                                                                                   

                                                                                    Video 3: Lion's mane jelly (Cyanea capillata)

            Some forms of jet propulsion affect feeding because some jellyfish can catch their prey while they swim, while others catch prey while remaining still. Jellyfish that chase after their prey are defined as cruising predators. Conversely, ambush predators remain still before 'snapping' on unsuspecting prey to quickly trap and kill their victims. With these different means of motion to the same end, cruising jellyfish form different wakes in their jet propulsion paths compared to those of ambush jellyfish. Cruising jellyfish have plural, symmetrical vortex rings while ambush predators have a single vortex ring followed by a jet of water. Cruising jellyfish expend less energy than ambush predators while hunting. This allows the cruisers to travel longer distances after their prey. The trailing jet of water formed by ambush predators has the high cost of expending a lot of energy, but creates larger kinetic energy in the wake. Ambush predators  only use jet propulsion to escape other predators or to migrate within the water column (Dabiri et al., 2010).

Drag Powered Swimming

            Fossilized seahorses are found very rarely, however, the ones that have been discovered support the hypothesis that seahorses have evolved from swimming in a horizontal position to an upright position. Fossils of seahorses found within the Indo-West Pacific date back to the Oligocene epoch 33.9-23.0 million years ago. During the Oligocene when this behavior evolved, global climates were cooling, sea levels were declining, and plates of the Earth's crust were shifting towards their current orientations. At this time, seahorses resided in shallower waters where seagrass is the dominant plant species. The upright position found in seahorses today most likely evolved because it allowed them to blend in using seagrass as camouflage against predators. This new, upright orientation amongst the ancestors of seahorses allowed them to maneuver quite well in these shallower areas (Teske & Beheregaray, 2009).

            Seahorses use fin undulation in their drag-powered mode of swimming. This is characterized by the movement of fluid along the fins that is caused by the oscillating motion of fin rays. Seahorses use both their dorsal and pectoral fins during undulation. The undulation of the dorsal fin in Weedy seadragon (Phyllopteryx taeniolatus) is seen in Videos 4 and 5. The fanlike bones that support the dorsal fin radiate from the spine to the outer dorsal skin and are known as pterygiophores. There are three bones that form the  dorsal fin: proximal radial, middle radial, and distal radial. Movement and oscillation of the fin rays are created by six pairs of muscles located on each fin ray (Consi et al., 2001).

Video 4: Weedy seadragon (Phyllopteryx taeniolatus)

                                                                                 
                                                                              Video 5: Weedy seadragon (Phyllopteryx taeniolatus)

            Seahorses have four fins: dorsal, anal, and two pectoral (seen in Figure 1). Although each fin undulates, the dorsal and pectoral fins are the only ones that create the propulsion for movement. Additionally, along with dorsal and pectoral fins, both the movable neck and muscular tail assist in steering. The undulations of the fins are caused by the phase-shifted oscillations of the fin rays, which create the movement of water over the fin from the anterior to the posterior side of the seahorse. This act of undulation forms eddies when water is moved over the posterior fins. These eddies interact with a jet of water allowing the seahorse to thrust forward. For motions that do not require a steering mechanism, the seahorse’s body is restricted to its median plane. The dorsal fin is also responsible for these motions and does so using bilaterally-placed inclinator muscles. These tiny dorsal and pectoral fins are only effective in transporting seahorses when the fin ray can sufficiently push through the viscous drag of the surrounding water (Consi et al., 2001).

 Figure 1: Seahorse anatomy portraying the dorsal,

 anal and pectoral fin locations (Consi et al., 2001)

Hydrofoil Swimming

              As seen in Videos 6 and 7, the forelimb, also known as the hydrofoil, is present as a swimming appendate in both the Magellanic penguin (Spheniscus magellanicus) and the Green sea turtle (Chelonia mydas), respectively. This limb acts as an aquatic wing characterized by a leading edge of stiff tissue and trailing edge of soft tissue. While swimming, the movement of the torso rotates the leading bone in the forelimb as the trailing edge follows behind. This hydrofoil propulsion swimming method is beneficial to penguins because it creates less noise in the water. This allows penguins in the wild to sneak up on their prey more efficiently. Additionally, hydrofoil swimming allows a great degree of flexibility in the forelimb for both penguins and turtles. The streamlined structure of the forelimb allows hydrofoil swimmers to spend less energy on drag when swimming against strong ocean currents. As seen in Videos 6 and 7, the hind limbs do not flap like the hydrofoils because the hind limbs function as rudders, maintaining the balance and swimming direction in hydrofoil swimmers (Xu et al., 2009).

Video 6: Magellanic penguin (Spheniscus magellanicus)

                                                                              
                                                                              Video 7: Green sea turtle (Chelonia mydas)

           Hydrofoil swimming form can be broken into four phases: pronation, downstroke, supination, and upstroke, with a 2:1:3:1 time ratio, respectively. Each of these phases is visualized in Figure 2. The pronation phase occurs when the forelimb reaches the upstroke’s peak, and continues around the extended axis to the peak of the downstroke. Next, the downstroke phase occurs when the hard leading edge of the forelimb sinks down. The forelimb then moves from the peak of the downstroke to its lowest point. Supination starts when the forelimb is at the downstroke’s lowest point. The forelimb then continues to move about its axis until it reaches the upstroke’s lowest point. Lastly, the upstroke phase starts when the leading edge points back upward. This orientation causes the forelimb to move from the lowest point of the upstroke to back its peak. These four phases form a figure-8 shape as also labeled in Figure 2. The upstroke and downstroke phases create a force of propulsion which allows the turtle to move forward. The positive and negative angles formed by the hydrofoil during the upstroke and downstroke are asymmetrical. The pronation and supination phases provide the turtle with constant movement as another advantage for the turtle to expend less energy  (Chu, Liu, & Xhang, 2007).

                                                Figure 2: Sketch of hydrofoil phases upstroke, 

                                                supination, downstroke, and pronation forming 

                                                a figure 8 (Xu et al., 2009).

Body-Caudal Fin Swimming

A. Anguilliform

            Marine species, primarily eels, that demonstrate anguilliform swimming have long narrow bodies, with a constant width from head to tail, that move by flexing their entire body. The body form and movement can be seen in the Zebra moray eel ((Gymnomuraena zebra) in Video 8. Anguilliform swimming minimizes the amount of energy on locomotion. During anguilliform swimming, circular vortices follow behind the fish. These vortices provide the swimmer with a constant thrust moving them forward while also decreasing the amount of drag. Some studies suggest that the anguilliform mode is approximately four to six times more energy efficient than the carangiform mode of locomotion (Neat & Campbell, 2013).

                                              
                                               Video 8: Zebra moray eel (Gymnomuraena zebra)

            During anguilliform swimming, the maximum curvature of the body gradually increases from the anterior to the posterior end. The positive and negative paired joint angles that occur throughout the body make the body shape curl down in the center of the body, causing the downward and upward turning motion.  Each segment of the body undulates around the same axis, which is known as the nominal line. The fish accelerates when the tail reaches the nominal line and the fish decelerates when the tail moves away from the nominal line. The net thrust is approximately the same as the net drag as defined by the constant speed of swimming. Both the tail and the anterior portion of the narrow body generate thrust for propagation. Thrust is generated constantly, primarily at the posterior end, while the drag is strongest at the head of the fish (Chen, Friesen, & Iwasaki, 2011).

            The tail of a Green moray eel (Gymnothorax funebris), seen in Video 9, produces two vortices each time it moves back and forth. When the tail moves in one direction, a stop-start vortex is formed. As the tail moves in the opposite direction, the back half of the body generates a low pressure system that causes surrounding water to flow laterally towards this pressure void. This laterally-flowing water flows off the tail and separates into two separate vortices. The diameter of the trailing jet continues to widen as the swimming speed increases. The velocity in which the tail is moving back and forth is the primary contributor to the kinetic energy within the wake. The circulation of the trailing vortices increases when the tail velocity increases, except when swimming at high speeds. At high speeds, the velocity reaches its maximum and levels off (Tytell, 2004). 

                                       
                                        Video 9: Green moray eel (Gymnothorax funebris)

B. Carangiform

            Fish that use the carangiform swimming form are characterized by having stiffer bodies and can swim at extremely high speeds. As seen in the Zebra shark (Stegostoma fasciatum) in Video 10, oscillation of the posterior end of the body and the high-aspect-ratio tail provides the thrust for locomotion. The flexibility of the caudal fins assists in propulsion and maneuverability. The sideways-flapping motion of the tail releases vortices into the fish’s wake. When the flapping motion of the tail changes direction, it pushes off of the previously shed vortex. This action of vortices-on-vortices causes them destructively interfere with one another to cancel each other. This decreases the drag that the carangiform swimmer experiences. Along with increasing swimming efficiency, this destructive interference also makes the swimmer quieter while hunting. This decreases the probability of a predator observing the fish’s wake. The upstroke of the tail forms a negative angle and the downstroke of the tail forms a positive angle with the water (Mason & Burdick, 2000). These upstrokes and downstrokes provide lift for the tail to power through viscous water. The lift through the water is then transferred to the rest of the body through the peduncle, which is the narrow portion of the body connecting the caudal fin to the rest of the body (Kelly et al., 1998).

                                      
                                          Video 10: Zebra shark (Stegostoma fasciatum)

C. Thunniform

            The force of thrust that moves thunniform swimmers through water is generated by a crescent shaped tail and peduncle. The streamline cross section of the caudal fin in thunniform swimmers is comparable to that of pectoral fins in hydrofoil swimmers. This thrust over streamlined caudal fins allows thunniforms to travel at high speeds, travel long distances, and minimizes the amount of kinetic energy transferred to drag. Due to the fact that the middle portion of a thunniform swimmer's body has a relatively large girth, recoil from the mid-section caused by the back and forth movement of the caudal fin is reduced. The thunniform swimming mechanism can be divided into two different models: resistive and reactive. The resistive model approach analyzes each part of thunniform swimming as a set of small, discrete stages, each with its own characteristic set of dynamic properties. The reactive model approach focuses on the momentum of the water displaced by an oscillating tail in thunniform swimming. By these definitions, resistive modeling suggests that inertial bodily forces are most important for motion while reactive modeling suggests that the thunniform propulsion is formed by vortices, their size, strength, orientation, and positioning.

            Because the tail is an elastic structure that can recover from deformation, motion of the caudal fin oscillating back and forth creates a high resistance against displaced water. The lateral and thrust forces generated by the caudal fin are asymmetrical because the tail shape itself is asymmetrical. Also, the flow of the water displaced by the caudal fin is asymmetrically distributed within the water column. This unique thrust provided by the caudal fin reduces the drag of the entire body. Accordingly, the generation of the forward thrust requires only a small amount of oscillations of the tail (Ben-Zvi & Shadwick, 2013).

Median Paired Fin propulsion

            A majority of stingray species use strict pectoral fin movement; however, other rays oscillate their pectoral fins in large up and down strokes to create vertical lift. The pelvic fins of skates contain large muscular appendages that allow them to take-off from beach sediments at the bottom of the water column. Although the pelvic fins of stingrays do not contain these muscular appendages, stingrays can still push off the bottom sediments in these same environments to assist their movements. In order for rays take-off from these locations, the anterior edges of the pelvic fins protract while the edges retract to push off the bottom.

            There is a correlation between the amplitude of undulatory waves and fin beat frequency and this relationship depends on the habitat of the stingray: benthic or pelagic. Benthic rays that reside on the beach floor flap their pectoral fins at a low amplitude with a high beat frequency. This allows them to maneuver well while swimming slowly along the bottom. This behavior is beneficial for hunting their prey on the sediment surface. Pelagic rays oscillate their pectoral fins using high amplitude waves and low fin beat frequencies. Benthic rays, such as the Cownose ray (Rhinoptera bonasus) seen in Video 11, do not extend their fins below their ventral body axes. This allows them to detect prey using their lateral line canals while also preventing contact of pectoral fins with the bottom sediment. Pelagic rays however have the ability to oscillate their pectoral fins both above and below the ventral body axis. As non-benthic predators, pelagic rays do not have to worry about hitting bottom sediments. For pelagic rays, the benefits of undulatory locomotion include the reduction of drag and increase maneuverability while swimming slowly. On the other hand, benthic rays have the benefit of oscillatory locomotion to increase vertical lift when swimming quickly; however, this method is not efficient for maneuvering (Maia, Wilga, & Lauder, 2012). 

     Video 11: Cownose ray (Rhinoptera bonasus)

            The muscles within the pectoral fins of thunniform swimmers do not work simultaneously. These muscles alternate in contraction, acting first in the anterior side and then in the posterior side. This is seen in the Mangrove whiptail ray (Himantura granulata) in Video 12. Additionally, the periods of contraction for fin muscles in thunniform swimmers vary as well, with ventral muscles contracting for longer periods than dorsal muscles. The power of the thrust is primarily created by the downstroke of the pectoral fin. The more intense the muscle contracts, the faster the swimming speed (Maia, Wilga, & Lauder, 2012).

 

             Video 12: Mangrove whiptail ray (Himantura granulata)

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