ACKNOWLEDGEMENTS
would like to thank my advisor Mark Denny for al his support.
guidance creative input, and just for being there when I was banging my
nead against a wall because l had no idea exactly what I was doing. I would
also like to thank Freya Sommer and the Monterey Bay Aquarium for help in
providing specimens.
ABSTRACT
The properties of fluid dynamics present interesting problems for
marine lise, dictating that the socomotion of slow moving animals are
controlled by the viscous forces in their environment. This study looked at
medu
an locomotion in adult and young Eutonina indicans. Medusae, unlike
many other emall marine organieme, maintain the same relative shape and
method of locomotion as their size spans 44 orders of magnitude during thei
growth phase. It was found that the locomotion oi the young medusae
dominated by drag These juvenie accelerate rapidy to overcome the
viscous forces inhibiting their motion, but decelerate just as rapidiy as thrust
tapers off. Medusae swim by a jet propulsion mechanism, in which they
produce thrust by ejecting fluid backwards. The aduits contract and
accelerate slower, but move more efficiently and further than the voung due
to their larger size. Over a similar time span and number of swimming
cycles the young onsy managed to move 1/3 the relative distance of the
adulte
INTRODUCTION
Fluid dynamics dictate that the smaller an object is and the slower it
moves the harder it is to move through a fluid. A dimensionless coeificient
called the Reynolds number (Re) quantitatively describes the effective
stickiness of the fluid -ie how difficult it is to push the fluid out of the
way
Re =ul/y
Uis the velocity of the fluid flowing by the object, 1 is some characteristic
length, andvis the kinematic viscosity of the fluid (Vogel, 1980). The
Reynolds number represents the ratio of inertial to viscous forces of a fluid
moving steadily past some object. For low velocity and small size, the
viscosity dominates and a low Reynolds number results, the opposite is true
for larger objects and objects traveling at high velocity
These properties present interesting problems for marine organisms
Medusae are particularly interesting in that, unlike many other organisms
that have various developmental stages with different methods of
locomotion, they maintain the same general shape and use the same method
of locomotion, even though they may undergo volume changes of four or
more orders of magnitude over their life. The subject of this study, Eutenin=
Igeans has typical volumes of less than 1 mm3 for the young and on the
order of 1 to 22103 mm3 for adulte. The adults have an inherent locomotive
advantage simply because their size allows them to operate at much higher
Reynolds numbers. The objective of this study is twofold: first to look at
general locomotion in the juveniles and aduits and see how and wy they
differ; second to look at the specific forces affecting a swimming medusa and
compare the strategies adopted by individuals of each size in dealing with
their respective situations.
MATERIALS AND METHODS
1 collected data by video recording captive medusae and then
performing a frame by frame analysis on the recorded information. Adults
were recorded in a display tank at the Monterey Bay Aquarium. These
animale were o-weeks old, and were the largest available specimens.
According to aquarist Freya Sommer, animals in the wild get much larger
due to their more varied diet. Because of their emaller size, recording the
juveniles which were less than 4 days of age, required the preparation of a
special tank Iconstructed a tant that was only 3/4 trom front to pack to
try to keep the animals in focus. The tank was lit irom above. The pack of
the tank was blackened and the front covered with polarizing film. All
animals were at 13°0.
The the first step in the analysis consisted of deciding which animals
of each size would be the subjects of the study. I watched the filmed
spécimens several times and also observed live animals to determine vnat !
will refer to as a typical jellyfish of each size -one that had no physical
abnormalities, and showed no aberrant swimming behavior. Once I found
appropriate specimens I traced the animal from a video monitor for each
trame three consecutive swim cycles. A swim cycle consists of a contraction
and an expansion. I traced each sequence 3 times as a means of estimating
tracing and measurement error. I also traced the distance the anterior
margin of the medusa traveled in each frame. The VCR records 30 frames
pe second soeach frame l traced represented 1/30 s. The spatial scaling
trom monitor to real life was 2:1 for aduits and 13:1 for the young
lused the distance data to construct plots of distance ys time. From
these data I casculated the velocity by taking a running average of the slope
of the distance data for any three points the slope at the middle one was
calulated by averaging the slopes of the lines to the points on either side
The forces involved in medusan locomotion can be summarized by the
following equation:

17
THRUSI - DRAG + ACCELERATION RXN + INERTIA (1)
Each of these forces can be broken down into simple physical parameters
which can be easily measured from the type of frame by frame analysis
described above (Daniel 1982).
Thrust T, the propulsive force in a jet locomotion system, is dependent
on the rate of momentum efflux from the animal(figure 1):
T - u. (dm/dt)
(2)
where u. is the velocity of the ejected fluid relative to the animal and
dm/dt is the rate at which mass is ejected from the medusa. Stated in other
terms thrust depends on the magnitude of the volume change, the rate of
volume change, and the size of the opening through which the fluid leaves,
For medusae this opening called the velar aperture(fig. 1). Equation 2 can be
rewritten as
T=/Ay)(dV/dt)2
(3)
in which is the density of seawater, 1025 kg/m3 Ay is the velar aperture,
and dV/dt is the rate of volume change. Velar aperture and the rate of
volume change are both potentially time varying. Velar aperture was
determined by taking diameter measurements from the video record, then
calculating the area by assuming the aperture to be circular. Volume
calculations were made by hand integration -l.e. I divided each tracing into
horizontal slices each of which reasonably approximated a cylinder, took a
méan radius and a height measurement of each slice, calculated the volume
of each slice, and then added the slices. The calculation of dV/dt was a
simple matter of taking a derivative of the volume with respect to time. For
simplicity of comparison volume, velar aperture, and the subsequent
measurements of projected surface area and the radius to height ratio were
graphed in the following way -since each animal was filmed for a sequence
of three cycles the three contraction phases were plotted together and the
three expansion phases were plotted together. Linear regressions were then
performed on each parameter for each size, so that rates of change could be
easily illustrated for young and adult.
Drag D, force always resists motion of the animal and is dependent on
the shape and speed of the animal.
D=C4005 S u?
(4)
Cais the drag coefficient, a dimensionless term which is estimated by the
equation (Daniel 1982)
Ca = 24/Ren
Re is the Reynolds number, the power n'is 1.0 for Recl and 7 for 1eRe6500.
Figure 2 shows Re versus time for both specimens, and they both fall in this
range.
S in Eq. 4 is the projected surface area (PSA) in the direction of motion
and uisthe instantaneous velocity of the animal with respect to ite
surroundings. I measured the PSA by taking a maximum radius of the
medusa and calculating area as for velar aperture. The instantanequs
velocity was calculated as described earlier.
The acceleration reaction(Eq. 1), like drag, is a shape-dependent force:
G =V du/dt
(6)
Note that G depends on volume rather than area, as for drag. Alpha is the
added mass coefficient -a term which reflects the effect of shape on the
acceleration of the surrounding fluid. It can be estimated by instantaneous
bell height, h, and radius, r:
a/h)l
(7)
Prolate (cigar-shaped) shapes have lower than do oblate (Mal) shaped
objects. Du/dt is the acceleration of the animal relative to the surrounding
fluid
Inertia is closely related to acceleration reaction, in fact G can pe
viewed as the effective inertia of the surrounding fluid. The sum of the
accelération reaction and inertia is the total force required to accelerate the
animal in the absence of drag:
F= (1)V du/dt
(8)
As opposed to drag, which always resists the motion of objects, these forces
resist changes in velocity
RESULTS
The distance vs time data shows that adults always maintain forward
motion while the young fall back between phases(figs 3&4). The velocity of
the adult and of the young both oscillate in the expected manner -reaching
maximum relative velocities durng the contraction phases. The adult data
show a net increase in velocity over the three cycles. The young accelerate
rapidly to a peak and then decelerate and actually attain a small negative
velocity between contractions. There is no accumulation of velocity as with
the aduits (fig 5). The drag coefficient for the adults is very stable in the
range of 0-1. For the young, Ca changes dramatically, often reaching values
o1 50 to 100. Negative values simply mean that the animal was moving in
the opposite direction(fig. 6).
Aduits onsy change their volume by twenty percent during contraction
as opposed to the seventy to eighty percent change in the young(fig. 7) The
young animals reach minimum volume in about 1/4 the time of the adults
and reexpand in 1/4 to 1/5 the time(figs 8 &9).
The differences in the change in velar aperture between juveniles and
adults are not as dramatic as those for volume. Adults undergo a 608
reduction as opposed to the young animal's 808 reduction(fig. 10). Once
again the time course for contraction and expansion in the young is about
1/4 that for the adult(figs. 1 1& 12). The absolute numbers for the thrust
calculations are not important as the calculations were made from linear
approximations of dV/dt and Ay In fact, these values actually taper as the
end of a contraction approaches, but the relative time course and the relative
accelérations are significant. Once again we see a factor of four difierence in
time course and also a maximum acceleration attained by the juveniles 4x
greater than that of the adult(figs. 138 14).
The young change their projected surface area by eighty percent
during contraction while the adults change by only 258 (fig 15). The
fourfold difference in time is evident once again (figs. 168p; 17). The drag
force resembles the velocity data in time and relative magnitude, it peaks
when velocity peaks and the difference between the maximum and
minimum values is the same. This indicates that velocity is the governing
parameter influencing drag (fig. 18). The adult added mass coefficient is
always greater than that of the young, while the two fluctuate by the same
amount (figs. 19,20&a;2 1).
The adult velocity (in bodylengths/s) is constant relative to the
immense fluctuation in the young (fig. 22). Over the course of three cycles
the young only move about 1.2 bodylengths and the adults move about 3
(fig. 23).
DISCUSSION
The continuous increase in the adult velocity reflects the reduced drag
effects the animals experience. The reduced drag is a result of two factors;
the lower Reynolds number at which the adults exist because of their size
and the fact that their greater mass allows them to maintain some forward
inertia during the expansion phase The young, on the other hand, due to
their smaller size and much larger drag coefficient, are dominated by drag
They have very littie inertia to carry them forward, and stop all forward
motion within a third of a second of the end of the contraction phase. In
terms of energetics, these conditions greatiy favor the adults. Energy
expenditure translates into acceleration due to the dependence of
acceleration on velocity change. Since the adult animals maintain some
forward velocity from prior contractions they can accelerate slower as they
approach some target velocity. In other words, adults can use a series of
contractions with smaller accelerations to gather speed. The advantage in
thie is that they don’t need large accelerations which would produce large
inetilforces acting against them. The young, however, face each
contraction with the same situation -to propel forward from a net negative
velocity. The jellyfish does a number of things to try to deal with this
situation:
Firstly the young accelerate themselves with a thrust force that peaks
four times sooner than the adust's and gives them four time greater
acceleration(figs. 13814). They accomplish this by throwing back 3 times
more of their total volume through an opening that closes to a relative size
1/3 times smaser that of the adult in 1/4 of the time.
The four fold time difference is a common theme in the time course of
all the time varying factors between young and adult, it reflects the
advantage the adults have in their low drag and larger mass. They can
afford to do things slower to avoid the negative influences of inertia and the
acceleration reaction, and thereby spend less energy swimming.
The dramatic changes the young undergo in shape and velocity
during contraction have several important consequences. The rapid
acceleration allows them to achieve their maximum forward velocity quickly,
First and most importantly this increases the Reynolds number at which the
ansmals are functioning assowing them to overcome the viscous forces of
drag. Unfortunately, velocity is a two edged sword, while increased velocity
inceases Re and lowers Ca drag itself is proportional to the square of the
velocity. As speed grows, so does the drag force which begins to dominate as
thrust tapers off. This seems contradictory, in that as speed increases the
drag situation becomes better and worse at the same time. The clarification
lies in the magnitude of the components that affect drag. Caand PSA both
decrease in time over the contraction phase, while velocity increases, so it
comes down to a question of dominance. Cq varies roughly lineariy with
velocity whereas overall drag varies with velocity squared,
The overall greater added mass coefficient of the adults (fig 19) is not
that great a burden to them due to the fact that they need not accelerate
that rapidly to increase their velocity -they combat inertial forces by using
small accelerations. The much lower, values for the young are crucial to
them as they must accelerate rapidly to try to get the most out of each
thrust.
Figures 22a;23 sum up the overall situation of the young medusae as
compared to the aduît animals. Despite their ability to accelerate to much
0
greater relative velocities, the young only net 1/3 the relative distance of
the adults for the same time period and number of contractions.
C
AV—
HOHENTUN
FIGURE 1

THRUST DRAG ACCEL.
RXN

IHERTIA
REYNOLDS NUMBER VS TIME
500

400
ADULT


300-



0


200


E

100
YOUNG
0
-100
40
10
20
30
50
TIME (SEC/30)
FIGURE 2
60
40
30
20
10
O-

20
DISTANCE VS TIME ADULT
40
TIME (SEC/30)
FIGURE 3
60
80
C
10
DISTANCE VS TIME YOUNG
30
TIME (SEC/30)
FIGURE 4
20
40
50
60
50
40
30
20
104
-10—


10
20
VELOCITY VS TIME

30
TIME (SEC/30)
FIGURE 5
ADULT
40

60
Cd VS TIME
100-
otaaaaaa-
-100
200—
10
30
20
TIME (SEC/30)
FIGURE 6
ADULT
YOUNG
40
—
50
60
7 MAX VOLUME

8
ADULI
5
06
04
YOUNG
02
0.0
20
30 40 50 50
TIME (SEC/30)
FIGURE 7
VOLUME VTIME - ADULT
2000
Sog
1800

Po

kaaaaa-
1600-
D

D

1400


1200 —
10 20 30 40 50 60
TIME (SEC/3O)
FIGURE 7a
VOLUME VTIME - YOUNG
1000
D
90
* 800
D
600


400
0
E

200
0 2 4 6 8 10 12 14 16 18 20 2224
TIME (SEC/30)
FIGURE 7b
% MAX VOLUME - CONTRACTION PHASE
10


0.6
ADULT
0.4-
2 YOUNG
0.2 -
0.0-
2
10
TIME (SEC/30)
FIGURE 8
ADULT CONTRACTION PHASE
2000
8
= 1800
y -2010.5 -74067x R°2=0915


1600

1400
1200
8
10
TIME (SEC/30)
FIGURE 8a
YOUNG CONTRACTION PHASE
1000
X 800-
y = 1202.2 -318.67X R°2 =0945
600
400
200 -
TIME (SEC/3O)
FIGURE 8b
1.0
0.8
0.6
0.47
0.2
0.0—
YOUNG

2
% HAX VOLUME - EXPANSION PHASE


ADULT

8
TIME (SEC/30)
FIGURE 9
10
12
2 MAX VELAR APERTURE
10
W
0.8

ADULT
0.6




0.4
0.2
YOUNG
0.0—
20
30
10
TIME (SEC/3O)
FIGURE 10
40

50
60
1.07
0.8
0.6
0.4
0.2
0.0
8 MAX VELAR APERTURE - CONTRACTION PHASE
ADULT
4
4
YOUNG
4
2
6
TIME (SEC/3O)
FIGURE 11
10
1.0
0.8
0.6
0.4
0.2
0.0
0
2 MAX VELAR APERTURE - EXPANSION PHASE



. .
4 4
4
TIME (SEC/30)
FIGURE 11
10
8
YOUNG (X 10--7)

2
THRUST VS TIME
TIME (SEC/30)
FIGURE 13
ADULT (X 10--5)
—
200
100
o
THRUST/MASS (ACCELERATION)
YOUNG (X 10)

ADULT
TIME (SEC/30)
FIGURE 14
1.0
0.8
0.6
0.4
0.2
0.0-
10
PROJECTED SURFACE AREA VS TIME
ADULT
VOUNG
30
40
20
TIME (SEC/30)
FIGURE 15
50
60
1.0
0.8
0.6
0.4
0.2
0.0 +
a
% HAX PSA VS TIME - CONTRACTION PHASE
N
4
A ADULT

YOUNG
TIME (SEC/30)
FIGURE 16
10
1.0
0.8
0.6
0.4
0.2
0.0+-
7 HAX PSA VS TIME - EXPANSION PHASE

4

YOUNG

1
ADULT

TIME (SEC/3O)
FIGURE 17
8
67

o
10
DRAG VTIME
ULTIX 10-5)

YOUNG(X10—-7)
30
20
TIME (SEC/30)
FIGURE 18
40
50
60
0.8
0.6
0.4-
0.2
0.0—
10
ADDED HASS COEFFICIENT VS TIME
ADULT
YOUNG
40
30
20
TIME (SEC/30)
FIGURE 19
50
60
0.8
0.6
0.4
0.2
0.0
ADDED MASS COEFFICIENT - CONTRACTION PHASE
4

1 .

4
ADULT
YOUNG
2
4 6
8
10 12
TIME (SEC/30)
FIGURE 20
0.8
0.6
0.4
0.2

0.0—
ADDED MASS COEFFICIENT - EXPANSION PHASE



ADULT
YOUNG
8
TIME (SEC/30)
FIGURE 21
10
10
8
ELOCITY IN BODYLENGTHS/SEC
YOUNG
VADT




10 20
30
40
TIME (SEC/30)
FIGURE 22
50

60
2
DISTANCE V TIME - BODYLENGTHS
ADULT/


YOUN6
O
10
40
20
30
TIME (SEC/3O)
FIGURE 23
50
60
LITERATURE CITED
Daniel, Thomas Louis (1982). The Role of Added-Mass in Impuisive
Locomotion with Special Reference to Medusae (Unpublished PHD.
Department of Zoology, Duke University).
Vogel, Steven. Life in Moving Fluids, (Boston, Mass. W. Grant Press, 1980).