Abstract
Organisms on rocky intertidal shores must withstand water velocities
of 10 to 20 m/s (Denny 1988, Carrington 1989, Jones and Demetropoulos 1968)
and accompanying accelerations of 400 m/s2 (Denny et al. 1985, Gaylord et al.
in press). Because drag and accelerational forces increase with area and
volume respectively, the bigger a species is, the larger the forces on it become.
Egregia menziesii is an unusually large alga that lives in the intertidal region
amid violent water motion. Here, I address how E. menziesii interacts with
flow. A hydro-mechanical model is used to predict the magnitude of the
forces on E. menziesii in various wave conditions and for various plant sizes.
Based on measurements of the strength of E. menziesii, an intact, average¬
sized plant's survivorship in the range of predicted wave forces is found to be
nearly 100%. However, predation and entanglement with other plants can
lower an individual's chances of surviving a severe storm to nearly 70%. E.
Menziesii's straplike shape is found to be necessary for accommodating the
distribution of tensions along the plant's stipe and for reducing drag.
Introduction
Wave induced water velocities on rocky shores can reach 10 to 20 m/s
(Denny 1988, Carrington 1989), and the accompanying accelerations can exceed
400 m/s2 (Jones and Demetropoulos 1968, Denny et al. 1985, Gaylord et al. in
press). Intertidal species have had to develop a range of strategies to survive
the extreme hydrodynamic forces that result from this violent water motion.
There are four forces that act on algae in waves: drag, lift, buoyancy
and an accelerational force. (Denny 1988, Koehl and Wainwright 1977
Gaylord et al. in press, Utter in preparation) Of these, drag and accelerational
forces are usually the largest. Drag, Eq, is the result of a pressure difference
between the fluid upstream and downstream of the plant (Vogel 1981). Drag
acts in the direction of flow, and is described by the equation:
Ed -(1/2) CdpAc ur ur.
(eq. 1)
where Cd is the coefficient of drag, p is the density of the water (1025 kg/m2
for seawater), Ac is the area of the plant, and ur is the velocity of the water
relative to the plant (Gaylord et al. in press).
The accelerational force, Ea, is the name given to the forces that result
from both the plant's and the water's acceleration (Denny 1988, Koehl 1986). It
is a combination of the force required to accelerate the mass of the plant itself,
and the forces which result from the acceleration of the water surrounding
the plant. Like drag, the acceleration reaction force acts parallel to the
direction of flow, and is given by:
Ea = M(du/dt) +pVCa(d(ur)/dt) +pY (du/dt),
(eq. 2)
where Mis the mass of the plant, uo is the velocity of the plant relative to the
stationary subtratum, u is the velocity of the water relative to the substratum,
p is again the density of the water, V is the volume of water displaced by the
object, and Ca is the added mass coefficient which indicates how much water
or "added mass" is accelerated with the plant (Gaylord et al. in press).
Several mechanisms by which some algae avoid being broken or
dislodged by these hydrodynamic forces have been studied. Gigartina
exasperata, for example, reportedly takes advantage of the boundary layer next
to the substratum in which water velocities are lower than in the mainstream
flow. By being flexible and lying near the substratum, this species exposes
only its upper surface to high flow velocities and reduces the amount of skin
friction drag that it experiences (Koehl 1984). Nereocystis luetkeana forms a
bundle of its blades, which reduces drag because of the bundle's streamlined
shape and because the blades on the inside of the bundle are shielded from
the largest water velocities (Koehl and Alberte 1988). Mastocarpus papillatus
reconfigures its branches in high water velocities to achieve a more
streamlined shape and thereby lowers its drag coefficient as flow increases
(Carrington 1990). Many other algae, such as Durvillea antarctiça, use
flexibility and extensibility, bending with the flow and then stretching
substantially before failing. Öthers, such as Lessonia nigrescens, are stiffer, so
they do not freely bend. Instead, they are stronger than many more flexible
algae, and this strength allows them to resist breakage (Koehl 1984).
Another technique for withstanding hydrodynamic forces has been
described in large algal species that grow subtidally, where water is calmer
than it is in the surf zone (Denny 1988, Gaylord et al. in press). If plants are
long enough, they can move with the water without ever becoming fully
extended and thereby avoid most of the potential drag (Koehl 1986). In
oscillating flow, a very long, flexible plant could reverse directions with the
water before ever using up the slack in its stipe (Koehl 1986). According to
this strategy of "going with the flow," bigger is better; the larger a plant is, the
less force it experiences.
Alternative scenarios are possible, however. Because drag increases
with an object's area, and the accelerational force increases with an object's
volume, it has been suggested that these forces could serve to limit the size of
wave swept plants (Gaylord et al. in press, Koehl 1986). According to this
explanation of how plants survive, smaller is better. Indeed, Gaylord, et al.
have shown that three species of algae, Gigartina leptorhynchos, Pelvetiopsis
limitata, and Iridaea flaccida, all have average sizes consistent with those that
would be predicted if drag and acceleration forces were limiting their size.
These plants are all less than 25 cm in length, so one might be led to believe
this is the ideal size for algae.
At present, it is not clear whether all algae's survival mechanisms can
be explained by one of the scenarios described above. For example, on rocky
intertidal shores, adjacent to the algae reported to be size-limited, is E.
menziesii, a plant that can be more than an order of magnitude larger than its
neighbors. E. menziesii is a brown algae that grows from Alaska to Baja
California on intertidal shores and at depths up to 20 m (Abbot and
Hollenberg 1976). An E. menziesii plant typically has 4-25 branches that can
grow to be 5 to 15 m long (Abbot and Hollenberg 1976). These branches
consist of stipes that have uniform, elliptically-shaped cross-sectional areas
throughout most of their lengths. The stipes are lined with blades of 2 to 8
cm on either side and, in some cases, with pneumatocysts (see Figure 1).
Approximately 25 cm from the end of each branch, or frond, there is a 1-4 cm
section of stipe without blades. Distal to this section, the stipe is flatter and
thinner and the blades on it are smaller. This last portion of the frond is the
terminal lamina.
E. menziesii's unusual size raises questions as to how it functions in
shallow wave-swept environments. For example: Does E. menziesii does
avoid drag by "going with the flow," as has been described for large algae in
deeper water? If so, is there any limit to the frond size it can support? Is E.
menziesii made of stronger material than other intertidal algae, or does it
have less frond area per stipe area? How large are the hydrodynamic forces
on E. menziesii?
Here, I address how E. menziesii interacts with flow. A hydro¬
mechanical model is used to predict the magnitude of the forces on E.
Menziesii in various wave conditions and for various plant sizes. These
forces are then compared to measurements of the strength of E. menziesii,
and predictions are made about the plant's survivorship. The hydrodynamic
model is also used to address the apparent advantages and disadvantages of E.
menziesii's unusual morphology.
Materials and Methods
Determining Breaking Strengths of E. menziesii
E. menziesii plants were selected haphazardly along the coast of Pacific
Grove, CA, to be tested for the forces required to break their stipes. If there
was visible evidence that a plant's stipe had been preyed upon, that
individual was not used. Each E. menziesii plant that was tested was first
given an exposure index based on its location. These ratings varied from one
to ten, where one was the most exposed and ten the most sheltered. The
ratings were determined by observing how many objects there were seaward
of the plant that would cause waves to break at the mid-tide level. Starting
with index = 1 indicating completely exposed, a point was added for each of
these wave barriers. For example, if there were three rock formations that the
waves passed before reaching a plant, then the plant was given an exposure
index of 4.
The breaking strength of each E. menziesii plant was then measured
with a spring scale. The scale was calibrated with standard weights before use
and was rechecked periodically throughout the study. A rope was attached to
the spring scale and then knotted around a plant's stipe 5-10 centimeters
above the holdfast. The scale was then pulled parallel to the substratum (to
simulate drag) until the stipe broke, and the maximum force registered by the
scale was recorded to the nearest 1.5 N. If the holdfast of the plant came off
the rock instead of the stipe breaking, the measurements for that plant were
not used.
The broken plants were taken back to the lab in sealed plastic bags.
There, the length and width of each broken stipe was measured within .05
mm with vernier calipers, and the cross-sectional area of the break was
calculated as an ellipse of the same length and width. The breaking strength
(that is, the force which broke the stipe divided by the cross-sectional area of
the stipe) was calculated for each plant. Fronds were then weighed and traced
onto paper, and the traces were cut out and weighed. The area of each frond
was determined by dividing the mass of each paper trace by the value for the
mass per square meter of paper. Once 160 fronds had been measured, an
allometric equation was fitted to the relationship between area, A (in m2), and
mass, M (in kg), of the plants using a simplex algorithm on the
untransformed data and a least-squares criterion for the best fit (see Figure 2).
The resulting equation:
A =0.05968 M0.8922
(eq. 3)
was used to estimate a value for frond area based on the measurement of
mass for the rest of the plants sampled.
When examining the breaking data for trends in the strength and size
of the plants at different exposure sites, all plants with an exposure rating of 5
were rejected. This was done to insure that there was a clear difference
between sheltered plants (rating 6-10) and exposed plants (ratings 1-4).
Once the two exposure groups were distinguished, an allometric curve
of the form y = a + bxc was fit to the measurements of plant strength and area
for each group. The strength data were then normalized to this curve by
dividing the actual force which broke a plant's stipe by the predicted breaking
force obtained from the allometric equation (eq. 7). This gave a value for
normalized breaking force (fn) for each plant. The fn values were ranked in
ascending order from 1 to N, where N was the number of plants tested in the
exposure category being analyzed. Estimates of the cumulative probability of
a plant having less than a given normalized force were found by the
equation:
p =i/(N+1),
(eq. 4)
where i was the rank of the plant. A modified Weibull function of the form:
p = exp Ia-bfn)/(a-bc)) 1/b
(eq. 5)
was then fit to these probabilities. The resulting equations were used to make
predictions of how likely it would be for a given force to break a plant of a
given area in each of the exposure categories (Denny and Gaines 1990).
While testing stipe strengths in the field, it was noted that many plants
already had broken branches. The remains of these former branches
resembled the stumps of stipe that were left after I pulled on them. To test
how many fronds were broken naturally, fifty plants (selected haphazardly)
from a range of exposures were examined. The major stipe branches on each
plant were counted, and then the fraction of these that were broken was
recorded.
Predicting Wave Forces on E. menziesi
A hydro-mechanical model (similar to that of Utter and Denny, in
preparation) was used to predict the stresses waves place on E. menziesii. The
model uses the shallow water approximations of linear wave theory to
describe water motion and treats a plant frond as a series of point masses
(nodes) connected by segments of extensible and flexible "rope" (see Figure 3).
Each node has a mass, M (equal to the mass of the frond segment which it
represents), and a buoyancy, B. The massless rope has the tensile strength,
compressive stiffnesses, and the cross sectional area of an E. menziesii stipe.
The force balance on each point mass, or node, is calculated as idealized
waves flow past the plant. The forces considered are those resulting from the
drag Eq, acceleration reaction Ea, buoyancy, B, and tension, T, of the stipe
proximal and distal to the node (see Figure 3). Lift is deemed to be negligible
in algae such as E. menziesii (Gaylord et al. 1990, in press) The forces at each
node are those that would be felt by the section of the frond which that point
represents. Treating the forces as vectors, the acceleration of each point is
determined. The basic equation by which the model operates is:
Ed+Ea+B+T=M(duo/dt)
(eq. 6)
where uo is the velocity of the point relative to the stationary substratum and
where all the forces are vectors. This equation is solved simultaneously for
all nodes using a fourth order Runge-Kutta algorithm and time steps of .0025
seconds. See Utter and Denny (in preparation) for further details.
A plant with average size and strength was selected and used to
determine the physical parameters for the model. The plant's terminal
lamina and rachis (see Figure 1) were separated, and each was used to describe
the corresponding section of the plant in the model. First, the rachis was
divided into sections of equal length. This length, L = 0.14 m, was the length
of the symbolic rope between the nodes of the rachis in the model. The
sections were then weighed, and the mean mass was used for M. The area of
a section was calculated by tracing as before, and used in calculations of Eq and
Ea. The drag coefficient that was also needed for calculations of Eq was
obtained by towing an E. menziesii plant behind a boat and measuring the
drag at different velocities (see Figure 4). The cross sectional area of the stipe
was measured with vernier callipers as before, and the resulting value was
used for the cross section of the rope. The same sequence of measurements
was made on the terminal lamina, which was divided into two sections of L =
0.12 m. These new values were given to the last two nodes in the model. A
value for the tensile strength was obtained from tests done by Buchanan
(1987, unpublished data). A small value for compressive stiffness was
estimated, so as to create reasonable behavior in the model.
Two values for buoyancy were used in the model. Most of the
intertidal plants observed in the field had a negative buoyancy, and six of
these were collected. A 0.14 m section was removed from each rachis. These
segments were weighed to the nearest 0.01 g, and their volume was
determined to the nearest 0.2 ml by water displacement. Their densities were
calculated from these measurements, and their buoyancies in sea water were
determined. The mean buoyancy, which was -0.02 N/node, was used in one
set of model runs.
A few plants were observed to be positively buoyant. To obtain an
estimate of the maximum buoyancy of intertidal plants, a plant with an
unusually high concentration of pneumatocysts was chosen, and its buoyancy
was calculated as described above. The value which resulted, 0.03 N/node,
was used in another set of model runs.
The buoyancies of the terminal laminas of all these plants were also
determined. They ranged from -0.015 to -0.025, and consequently the terminal
laminas in all the model runs were given a buoyancy of -0.02.
The model was first used to predict the forces due to a range of wave
heights on two standardized plants of identical dimensions: one plant was
negatively buoyant, the other positively buoyant. The two plants were placed
in simulated water 1.5 meters deep, which was judged to be a typical depth for
E. menziesii at high tide. The plants were then subjected to waves increasing
in height from .75 meters to 2.5 meters (approximately the maximum size
waves can become before breaking in water of this depth, Denny 1988) at .25
meter increments. The model was run for one wave period to allow
equilibration, and the maximum force felt by each node during the
subsequent wave period was recorded.
The program was then used to model the forces imposed by 1.5 meter-
high waves in 1.5 meters of water on plants of increasing sizes. Plants of -0.02
and +0.03 buoyancy were "grown" from 0.66 meters length, adding 0.14
meters (one node) at a time. Again, the maximum force felt by each node
during a wave period was recorded.
A graphics program was used to check the results of the model. This
program maps the location of each node at each time, drawing the E.
menziesii as it is moved by a wave. The computer's descriptions of the
motions of both positively and negatively buoyant plants were compared to
actual plants' motion in waves as observed from the shore and while
snorkeling.
Results
Breaking Strength
An analysis of the data for stress required to break each stipe for a given
plant size indicates that the mean strengths of exposed and protected plants
are statistically distinct (Mann-Whitney U test, nj=40, n2-39, U=1141, p«.001).
The stress required to break the stipes of exposed plants were correlated to the
plants' areas by the equation:
F = 102.613 + 365.868 (A)0.8223
(eq. 7)
where F is the force (in N) and A is the area (in m2) (Student's t-test, df-39,
pe.02). There was no significant correlation, however, between sheltered
plants' area and breaking force. The mean breaking force for sheltered plants
was 92.4 N (see Figure 5). The frond area per stipe cross sectional area was
correlated to exposure, increasing as exposure decreased (Student's t-test,
p«.02) (see Figure 6).
10
The parameters for the Weibull functions for the probability of
breaking (eq. 5) were: a = 0.3049, b = 0.0124,c = 0.8387 for exposed plants, and a
= 0.4685, b = -0.0036, c = 0.7562 for protected plants (see Figure 7).
There was no significant correlation between level of exposure and the
fraction of broken stipe branches (Student's t-test p»».05).
Model Results
The average and maximal forces predicted to be imposed on the 1.36 m,
negatively buoyant plant increase with wave height (see Figure 8). For wave
heights less than 1.5 meters, the maximum force occurs near the free end of
the plants. As wave height increases, however, the maximum force occurs at
the basal node (see Figure 9).
The predictions for the 1.36 m, positively buoyant plant are more
regular: force at every node increases with wave height, and force along the
plant decreases with distance from the holdfast (see Figure 10). The average
and the maximum forces predicted for the positively buoyant plant are less
that those for the negatively buoyant plant (compare Figure 8 and Figure 11).
For a given waviness, forces on E. menziesii increase as the plant
increases in size (see Figure 12). However, in negatively buoyant plants of
different sizes, the maximum forces are not always at the base, and large
forces appear at the base, the middle, and at the end of the stipe (see Figure
13). In positively buoyant plants, forces tend to decrease along the stipe even
as the plants get longer (see Figure 14).
Survivorship Predictions
The probabilities of a stipe of an intact plant breaking from the
maximum wave forces predicted were uniformly low. For a 1.36 m plant in
1.5 m water with 2.25 m high waves, which is the largest waves would
become without breaking, the probability of a stipe failing was 3.85 x 10-7.
11
Discussion
Tests of the breaking strength of E. menziesii indicate that it is much
stronger than it needs to be to withstand the hydrodynamic forces it
experiences. For example, the model predicts that the largest force on an
standard plant of 1.36 meters in 1.5 meters of water with 2.5 meter waves will
be 14.02 N. The strength per area relationship (eq. 7), however, indicates that
this plant requires more than 145 N to break its stipe. This means that the
plant is at least 10 times stronger than it needs to be to withstand even the
strongest expected wave, as a result, its chances of breaking 1 in 2.6 million.
The question then becomes, not how could E. menziesii possibly be strong
enough to survive the forces on it, but why is it so much stronger than it
seemingly needs to be?
Observation of actual E. menziesii plants in the intertidal zone
indicates why this strength may be necessary. E. menziesii is often preyed
upon by the limpet Notoacmea insessa. It is not uncommon for these limpets
to eat half way through E. menziesii stipes, decreasing the forces that plants
can withstand by at least 1/2. E. menziesii fronds also often become tangled in
each other, which could place the forces from many fronds on one stipe.
Koehl and Wainwright (1977) described such tangling as being a major cause
of stipe breakage in Nereocystis luetkeana, and it is also common among
Macrocystis pyrifera (P. Dayton, personal communication to M. Denny).
If the forces on 4 E. menziesii fronds are projected onto one stipe
because they are entangled, and if that stipe has been half eaten by limpets,
that plant can withstand only 1/8 the force it normally could survive. This
reduces the estimated stress required to break the stipe to about 18 N.
Inserting a normalized force of 14/18 into equation 5 (with the coefficients
determined for exposed sites) yields a probability of breaking of 29.2%. This
12
result indicates that E. menziesii may be designed so that they can survive
some level of predation and entanglement. If either of these factors becomes
too severe, however, the plant is in danger of being broken by a large wave.
E. menziesii's strength does not result from the material in its stipe
being stronger than that of other algae. E. menziesii's tensile strength is 1.2 X
107 (Buchanan, unpublished data), which is in the same range as other algae
(from 9.6 x 10° for Postelsia parmaeformis to 3.6 x107 for Iridaea flaccida,
Denny et al. 1989). E. menziesii's frond area per stipe cross-sectional area is
also in the same range as that measured for other algae. For example,
Carrington's (1990) measurements of Mastocarpus papillatus indicate that it
has a frond area per stipe area of about 2800. As Figure 6 demonstrates, E.
menziesii at exposed sites have frond areas per stipe areas averaging around
2000, and E. menziesii at sheltered sites have fond areas per stipe areas
averaging around 4000.
Some of the explanation for how E. menziesii attains its large size
could reside in its coefficient of drag, Cd (see eq. 1). In water velocities of 1.9
m/s, E. menziesii's coefficient of drag is 0.016 (from Figure 4 and eq. 1 with
measurements of the plant on which drag tests were done). In the same
conditions, M. papillatus's drag coefficient is 0.123 (Carrington 1990). This
means that, for a given area, E. menziesii experiences 7.7 times less drag than
M. papillatus. Thus, E. menziesii could be accommodating its large size by
streamlining its shape and thereby reducing its drag.
Another question that arises is why (unlike other algae) the stipes of E.
menziesii maintain the same cross sectional area throughout their length. If
drag forces added cumulatively along a plant, one would expect that the stipe
near the free end of the plant would experience less stress than the stipe at the
base. An analogy can be drawn to a chain hanging from a ceiling. The links
13
closest to the ceiling have the most force on them because they support the
weight of the whole chain. Those at the end, however, only support the
weight of the few links beyond them. If the drag forces on a plant were
analogous to weight on a chain, then the stipe area near the end of the plant
could be smaller and still maintain the same chance of breaking, and thus the
plant might show tapering along its length.
The fact that the stipes of actual E. menziesii do not exhibit such
tapering can possibly be explained by the predictions made by the model for
the forces on various size plants subjected to waves of constant height. Figure
13 shows that the maximum forces from a 1.5 m wave on negatively buoyant
plants of a range of sizes can be found at almost any point on their stipes. In
addition, Figure 9 shows how the location of the maximum force on a 1.36 m
plant moves along its stipe as wave heights vary. This is because, as an E.
menziesii plant moves in a wave, the plant curls up on itself. The motion of
the wave then unfolds this loop, and the unfolding results in a whiplike
motion. The portion of the plant that is "whip-cracked" experiences forces
that are often some of the largest forces resulting from the wave. Because the
position of the whip-cracking forces changes with length of plant and strength
of wave, the stipe must be strong all along its length.
This whip-cracking is seen to a lesser extent in positively buoyant
plants. As Figures 10 and 14 indicate, the largest tensions in positively
buoyant plants' stipes tend to be at their bases. The explanation given above
for the uniform stipe areas in E. menziesii therefore does not apply to
positively buoyant plants. Positively buoyant plants in the intertidal region
are rare, however, so it is possible that the species has developed to
accommodate negatively buoyancy.
14
A surprising result of the computer modeling is shown in Figure 12.
According to descriptions of large algae "going with the flow" and avoiding
drag (Koehl 1986), one would expect that the longer E. menziesii become, the
smaller the fraction of time plant will actually be stretched out in a wave, and
the later that time will be in the wave cycle. Because the water velocity from
waves follows a sinusoidal pattern, if a plant does not feel drag until later in
the wave cycle, the drag that the plant does feel will be smaller because the
velocity of the water will have decreased. As Figure 12 indicates, however.
this does not seem to occur. Up to the size plant which the model could
accommodate, the maximum forces predicted increased with plant size.
Although the model needs to be improved so that larger plants can be
studied, E. menziesii does not seem to display the mechanism described for
other large algae of improving their ability to withstand hydrodynamic forces
by increasing in length (Koehl 1986). It is possible that the curling of fronds
(prior to "whip-cracking") typical of E. menziesii prevents the plant from
smoothly going with the flow.
Subtidal E. menziesii tend to be positively buoyant, but a majority of
the intertidal E. menziesii studied were negatively buoyant. The model raises
the question of why negative buoyancies are observed in E. menzies
populations at all, because it predicts that, under the conditions tested,
buoyancy reduces the forces on E. menziesii (compare Figures 6 and 9). The
answer could be that a negatively buoyant plant is able to clear the substratum
around it as it moves in the waves, pushing away any competitors for space
with the motion of its fronds. For example, Laminaria pallida employs such a
sweeping mechanism to clear circular patches around itself (Velmirov and
Griffiths 1979). The advantage of keeping away competitors could be greater
than the advantage buoyancy provides in reducing the forces felt by the stipe,
15
especially given the apparently high safety factors exhibited by individual
fronds of E. menziesi
The forces required to break E. menziesii plants' stipes were found to be
correlated to the plants' areas in the exposed sites but not in the sheltered
sites. This could be explained two ways. First, the more exposed plants could
have already been "pruned" by the waves hitting them. Weaker sections of
plant would have broken off so that only the stronger sections remained to be
tested. In this scenario, selection for stronger branches of stipe would not
have occurred in the more sheltered plants where wave forces were less
strong. If this explanation were correct, one would expect to find a greater
proportion of broken branches in exposed than in sheltered plants. Such a
pattern was not observed.
The second possible explanation is that the plant's morphology
responds to the demands of its environment during ontogeny. Sheltered
plants would not experience forces as strong as those imposed on exposed
plants, and in response, their stipes would not develop to as great an extent.
Exposed plants would experience large forces, so they would develop larger,
broader stipes in response. There is much evidence that algae do indeed
adapt their morphology to environmental conditions. Laminaria longicruris
are observed to have strap-like blades on exposed coasts and broader blades on
sheltered coasts (Gerard and Mann 1979) Nereocystis luetkeana blades are
narrower and flatter at exposed sites than at sheltered sites (Koehl and Alberte
1988), and reciprocal transplant experiments by Koehl and Alberte (1988)
showed that when narrow, flat-bladed plants from exposed sites were
transplanted to sheltered sites the blades became wider and more undulate.
The plants that were transplanted from sheltered areas to exposed areas did
not survive. Gerard (1987) grew Laminaria saccharina under different stress
16
conditions, hanging weights from the ends of some plants and not others.
The plants with weights to simulate drag developed narrow blades
(characteristic of exposed plants), and the others developed wide blades
(characteristic of protected plants).
Conclusions
Intact E. menziesii plants are strong enough to survive the forces of
the largest expected waves, although their chances of breaking increase
substantially if their stipes are preyed upon or are twisted around each other.
Although individual plants are often large enough to "go with the flow,
model simulations suggest that E. menziesii does not employ this
mechanism of avoiding drag. Instead, E. menziesii minimizes the force on its
large fronds by streamlining its shape to reduce its drag coefficient.
Acknowledgments
I owe countless thanks to Mark Denny for all his help with this
research. He has been incredibly generous with his time and knowledge and
has guided me through every step of the project.
Molly Cummings, Sandy Friedland, and Tom Friedland also provided
vital assistance by joining me in pulling on Egregia plants. I could not have
faced all the 6:00 am low tides without them.
I would also like to thank Brian Gaylord for his work on the hydro-
mechanical model and for his patience with my questions throughout the
quarter.
Lastly, I would like to thank Kim Hoke and Ravi Chandrasekaran for
being wonderful housemates, cooking great food, and making this quarter
fun.
Literature Cited
Abbott, I. A. and G. J. Hollenberg, 1976. Marine Algae of California. Stanford
University Press, Stanford, California, USA. 827 pps.
Carrington, E. 1990. Drag and dislodgment of an intertidal macroalga:
consequences of morphological variation in Mastocarpus papillatus
Kutzing. Journal of Experimental Marine Biology and Ecology 139: 185-
200.
Denny, M. W. 1988. Biology and the mechanics of the wave-swe
environment. Princeton University Press, Princeton, New Jersey,
USA. 320 pps.
Denny, M. W., V. Brown, E. Carrington, G. Kraemer, and A. Miller. 1989.
Fracture mechanics and the survival of wave-swept macroalgae.
Journal of Experimental Marine Biology and Ecology 127: 221-228.
Denny, M. W. and S. D. Gaines. 1990. On the prediction of maximal
intertidal wave forces. Limnology and Oceanography 35: 1-15.
Gerard, V. A. and K. H. Mann. 1979. Growth and production of Laminaria
longicruris (Phaeophyta) populations exposed to different intensities of
water movement. Journal of Phycology 15: 33-41.
Gerard, V. A. 1987. Hydrodynamic streamlining of Laminaria saccharina
Lamour. in response to mechanical stress. Journal of Experimental
Marine Biology and Ecology 107: 237-244.
Jones, W. E. and A. Demetropoulos. 1986. Exposure to wave action:
measurements of an important ecological parameter on rocky shores
on Anglesey. Journal of Experimental Marine Biology and Ecology 2:
46-63.
19
Acknowledgments
I owe countless thanks to Mark Denny for all his help with this
research. He has been incredibly generous with his time and knowledge and
has guided me through every step of the project.
Molly Cummings, Sandy Friedland, and Tom Friedland also provided
vital assistance by joining me in pulling on Egregia plants. I could not have
faced all the 6:00 am low tides without them.
I would also like to thank Brian Gaylord for his work on the hydro-
mechanical model and for his patience with my questions throughout the
quarter.
Lastly, I would like to thank Kim Hoke and Ravi Chandrasekaran for
being wonderful housemates, cooking great food, and making this quarter
fun.
Literature Cited
Abbott, I. A. and G. J. Hollenberg, 1976. Marine Algae of California. Stanford
University Press, Stanford, California, USA. 827 pps.
Carrington, E. 1990. Drag and dislodgment of an intertidal macroalga:
consequences of morphological variation in Mastocarpus papillatus
Kutzing. Journal of Experimental Marine Biology and Ecology 139: 185-
200.
Denny, M. W. 1988. Biology and the mechanics of the wave-swept
environment. Princeton University Press, Princeton, New Jersey,
USA. 320 pps.
Denny, M. W., V. Brown, E. Carrington, G. Kraemer, and A. Miller. 1989.
Fracture mechanics and the survival of wave-swept macroalgae.
Journal of Experimental Marine Biology and Ecology 127: 221-228.
Denny, M. W. and S. D. Gaines. 1990. On the prediction of maximal
intertidal wave forces. Limnology and Oceanography 35: 1-15.
Gerard, V. A. and K. H. Mann. 1979. Growth and production of Laminaria
longicruris (Phaeophyta) populations exposed to different intensities of
water movement. Journal of Phycology 15: 33-41.
Gerard, V. A. 1987. Hydrodynamic streamlining of Laminaria saccharina
Lamour. in response to mechanical stress. Journal of Experimental
Marine Biology and Ecology 107: 237-244.
Jones, W. E. and A. Demetropoulos. 1986. Exposure to wave action:
measurements of an important ecological parameter on rocky shores
on Anglesey. Journal of Experimental Marine Biology and Ecology 2:
46-63.
19
Koehl, M. A. R. and R. S. Alberte. 1988. Flow, flapping, and photosynthesis of
Nereocystis luetkeana: a functional comparison of undulate and flat
blade morphologies. Marine Biology 99: 435-444.
Koehl, M. A. R. and S. A. Wainwright. 1977. Mechanical adaptations of a
giant kelp. Limnology and Oceanography 22: 1067-1071.
Koehl, M. A. R. 1984. How Do Benthic Organisms Withstand Moving Water?
American Zoologist 24: 57-70.
Koehl, M. A. R. 1986. Seaweeds in moving water: form and mechanical
function. In: On the economy of Plant Form and Function, T. J.
Givnish (ed.), Cambridge University Press, Cambridge, Great Britain,
PPS. 603-634.
Velimirov, B. and C. L. Griffiths. 1979. Wave-Induced Kelp Movement and
its Importance for Community Structure. Botanica Marina 22: 169-172.
Vogel, S. 1981. Life in moving fluids. Princeton University Press, Princeton,
New Jersey, USA. 352 pps.
Figure 1. Egregia menziesii, the species used in this study.
Figure 2. Area of E. menziesii increases with mass, according to relationship
in eq. 3. R2 = 0.959 for correlation between area predicted by eq. 3 and
actual area measured.
Figure 3. Representation of E. menziesii frond in hydro-mechanical model.
Each frond section is modeled as a point mass (node) acted upon by
vector forces. The point masses, which occur at the nodes, are
connected by a flexible, extensible "rope" that simulates the stipe.
Figure 4. Measurements of the drag force were taken from an E. menzie
plant which was towed behind a boat. Water velocities are relative to
the plant.
Figure 5. Force required to break stipe is correlated to frond area in plants at
posed sites (eq. 7) but not in plants at protected sites.
Figure 6. The frond area per stipe cross-sectional area (q) varies with exposure
index (s) by correlation equation: qu = 1419.623 + 307.377 (s).
Figure 7. Weibull functions for probability of breaking can be used with
estimates of forces from waves to predict a plant's survivorship.
Figure 8. Maximum tension at any node and average tension on all nodes of
a negatively buoyant,1.36 m plant increase with increasing wave height
(in water 1.5 m deep).
21
Figure 9. Tensions at nodes of a negatively buoyant, 1.36 m plant as wave
height increases in water of 1.5 m. At waves below 1.5 m in height, the
largest force is near the free end of the plant. In waves above 1.5 m, the
largest tension is at the base of the plant.
Figure 10. Tensions at nodes of a positively buoyant, 1.36 m plant as wave
height increases in water of 1.5 m. The largest tension is always at the
base of the plant.
Figure 11. Maximum tension at any node and average tension from all nodes
of a positively buoyant, 1.36 m plant in 1.5 m water increase as wave
height increases.
Figure 12. Maximum tension in positively and negatively buoyant plants
increases as they increase in length, which would not be predicted if the
plants were "going with the flow" to reduce drag.
Figure 13. Large tensions are predicted at points all along the stipes of
negatively buoyant plants, which could explain why the stipes
maintain the same cross-sectional area throughout their lengths.
Figure 14. Unlike negatively buoyant plants, positively buoyant plants
experience the most tension near at the base of their stipes.
22
Pneumatoc
ane
Lamina
Frond
20 cm
L
2
Stipe
Rachis
Holdfast
e
0.070
0.060
0.050
0.040
50.030
I
0.020
0.010
0.000
0.00
2


0.03
9
0.06
0.09
Mass (kg)
0.15
0.12
Fgurea
Buoyancy, B
o.
Node +.
6 9
57
4
ATension, 7
Accelerational Force, F.
Drag, F.
Tension, I
gore
S
....
.

Drag (N)
o8

(:*
8.
*:.
S
Figere
O
300
250
200
150
100
50

+
O
Exposed

D
5

o

O
L t


D
+ +-Protected
t
+ +
++
++ +

0.10
0.00
0.05
0.15
Frond Area (m2)
Hga

D
0.20
10000
8000
0
8 4000
2000


D
D

0 1 2 3 4 5 6 7 8 9
Exposure Index
Fgue(
1.0
0.9
0.8
20.7
0.6
O.
90.4
O.3
0.2
0.1
0.0
O.0
Exposed-
1.5
1.0
Normalized Force

Protected
2.0
Hgur 7
2.5
I

Maximum
Wave Height (m)
Average
15
10
Negatively Buoyant
Hgr 8
2
Negatively Buoyant


44
V—V
4.
8.
2
Wave Height (m)

Node
- □—1
--+-- 2
--0-- 4
A 6
—0- 8
-V- 10
Ggue d
15
12
Positively Buoyant

Wave Height (m)
Node
- +-1
--+-- 2
--O-- 4
A 6
-0- 8
—V- 10
Ggore
D
Positively Buoyant
Maximum
/Average
2
Wave Height (m)
gol
Neg
D
gatively Buoyant
D
+ +
D
Positively Buoyant
+
Length (m)
Hgore 12
2
2
+--++
L
Negatively Buoyant
4
0-9
+


12
Node Number
Hu
Positively Buoyant

A

0--0
+-..+
L

12
Node Number
Ho