The mechanics of wave-swept algae
1 Hopkins Marine Station of Stanford University, Pacific Grove, CA 93950,
USA
2 Department of Ecology, Evolution, and Marine Biology, University of
California, Santa Barbara, CA 93106, USA
* e-mail: mwdenny{at}leland.stanford.edu
Accepted 1 March 2002
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Summary |
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Key words: marine alga, ocean wave, kelp, intertidal zone, hydrodynamic force, material properties, nearshore ecology
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Introduction |
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How are organisms designed to survive in these sorts of extreme environments? To put the question in the context of our analogy, how would the morphology of sylvan plants and animals have evolved if every 10 s or so a hurricane-strength breeze or a gust of supersonic wind roared through the forest? In most cases, the animals of wave-swept shores resemble what one might intuitively expect small, armored individuals firmly attached to the ground. A limpet, for instance, has a body contained within a rigid, streamlined shell and adheres to the rock's surface with a relatively huge, glue-covered foot. A sea star has a body that can periodically be softened to conform to the shape of the substratum, but then hardens in place; the resulting armored structure is held down by hundreds of tube feet. In both cases, the organisms are quite small. As one might expect, collecting wave-swept animals is often a job requiring pry bars and chisels.
In contrast, wave-swept marine algae are a surprise. With few exceptions,
they have eschewed the strong, stiff armor typical of nearshore sessile
animals and are constructed instead of weak, compliant materials. Collecting
marine algae is often simple score a plant with a thumbnail and it
practically falls off the rock. Furthermore, wave-swept algae occur in a
myriad of shapes, few of which appear to be classically streamlined. The
common morphological theme seems to be flexibility rather than protection,
which (as we will see) can have both advantages and disadvantages. And, while
many wave-swept algae are of a small size similar to that of the co-occurring
animals, some (e.g. the giant kelp Macrocystis pyrifera) are quite
large, reaching lengths of more than 30 m and masses in excess of 50 kg
(Foster and Schiel, 1985).
How can we account for the non-intuitive design of wave-swept plants? In recent years, the general outline of a story has emerged that provides insight into how evolution has responded to the exigencies of a uniquely stressful environment. This information may have practical utility in evaluating how these ecologically and economically important plants will respond to predicted changes in the wave climate of the ocean.
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Algal morphology |
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As noted above, this basic body plan allows for an immense diversity of
shapes (see, for example, Abbott and
Hollenberg, 1976; Druehl,
2000
). Some algae have no fronds and exist as a simple crust on
the rock. Some have unbranched stipes, while others branch repeatedly. Blades
may be simple, two-dimensional, strap-like sheets or complex,
three-dimensional frills. In many of the large brown algae (in particular,
many kelps), fronds may include one or more gas-filled floats termed
pneumatocysts. These floats help to ensure that the blades are held as near as
possible to the surface of the water, where light is most intense and
photosynthesis is thereby enhanced.
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Flexibility: the role of materials |
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The flexibility of algal fronds is due in part to the properties of the
materials from which the fronds are constructed. In general, both stipes and
blades are made from materials that have a low stiffness and a high
extensibility. Typically, stiffness (=elastic modulus, E) is within
the range 1-100 MPa (a bit stiffer than rubber and less stiff than tendon),
and these algal materials can be extended by more than 10 % (a strain >0.1)
before they break (Koehl,
1986; Denny et al.,
1989
; Hale, 2001
).
Even the `woody' stipe materials are relatively compliant. For example, the
stipe of Eisenia has a modulus of only 60 MPa
(Gaylord and Denny, 1997
),
well below the stiffness of wood (10 000 MPa;
Wainwright et al., 1976
).
(Note that `woody' algal materials contain no real wood; they have neither
xylem nor phloem and their cell walls are not lignified.) Algal materials also
differ from wood in that their stiffness in tension is often considerably
higher than their stiffness in compression
(Biedka et al., 1987
;
Holbrook et al., 1991
;
Gaylord and Denny, 1997
). This
often-overlooked feature has the potential to affect strongly the stress
distributions developed in the tissues of some species
(Gaylord and Denny, 1997
).
Coralline algae are characterized by calcified cell walls, and their materials
can thereby be both stiff and inextensible. However, articulated (as opposed
to crustose) corallines have uncalcified `joints' (geniculae) in their fronds,
which allow these plants to flex back and forth.
The energy per volume that a material can absorb before it breaks (strain
energy density, J m-3) is proportional to the product of the
elastic modulus and the breaking strain. As a result, the low stiffness of
algal materials tends to offset their high extensibility, and their strain
energy density is typically within the range 0.1-1 MJ m-3
(Hale, 2001). This is 10- to
100-fold lower than that of materials such as collagen and the protein rubbers
(elastin, abductin, resilin), and 100- to 1000-fold lower than that of mussel
byssal threads and spider silk (Hale,
2001
).
Algal materials have a low work of fracture (0.2-3 kJ m-2)
(Biedka et al., 1987;
Denny et al., 1989
;
Hale, 2001
) and, like all such
materials, are susceptible to breakage by the propagation of small initial
flaws. For example, a pane of glass is easily broken by first scoring it with
a diamond stylus. Similarly, if one bends the stipe of a kelp and makes even a
small cut at the outside of the bend, the stipe breaks catastrophically. This
is the basis for the ease with which kelps can be collected, noted above.
[Note that the work of fracture values reported in Biedka et al.
(1987
) and Denny et al.
(1989
) must be multiplied by 4
(Hale, 2001
).]
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Structural flexibility |
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The nearshore flow environment |
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Flow prior to wave breaking
In unbroken waves, the pattern of flow (as predicted by linear wave theory)
(Kinsman, 1965;
Denny, 1988
) is determined by
the wave height, the depth of the water column and the wave period,
T. The inter-relationship among these variables is complicated, but
there are two points common to all waves. First, water particle velocity (as
distinct from the velocity of the waveform) is directly proportional to wave
height: the higher the wave, the faster the flow. Second, for any wave period,
the shallower the water column, the higher the orbital speed
(Fig. 1).
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Fig. 1 also exposes two fundamental differences between flow at the surface and flow at the substratum. First, for a given wave period, as the water column gets deeper, flow at the surface asymptotes to a fixed, positive velocity (best seen for T=5 s in Fig. 1A) while, in contrast, flow at the substratum asymptotes to zero (see the line for T=5 s in Fig. 1B). In other words, if the water column is sufficiently deep (or the wave period sufficiently short), algae living near the sea floor can avoid wave-driven flows, whereas algae whose long stipes and buoyant pneumatocysts allow them to reach the water's surface must always contend with the waves. (Note that, although the water velocity at the surface is always greater than that at the seafloor, for water column depths less than approximately 5 m the difference is slight.) Second, for any water column depth, flow depends on the wave period. For flow at the substratum, the longer the wave period, the higher the velocity. For flow at the surface, the longer the wave period, the lower the velocity.
An example is perhaps in order. Ocean swells on exposed shores typically have a period of 10 s and a height of 2 m. Given these values and a water-column depth characteristic of giant kelps (20 m), the maximum velocity at the surface is 0.8 m s-1, while at the substratum it is only 0.5 m s-1. At a shallower depth near the point of breaking (2 m), the velocity at the surface has increased approximately fourfold to 2.3 m s-1, a value that is nearly matched by that at the sea floor, 2.2 m s-1.
The velocity imposed by an unbroken wave varies with position relative to
the waveform speed of flow is maximal under the crest and trough.
However, given the large wavelengths typical of ocean waves (tens of meters)
(see Eckart, 1952;
Denny, 1988
), the rate of
spatial variation in velocity is small, and velocity is nearly constant along
all but the longest fronds.
The acceleration of water in an unbroken wave can be calculated from linear
wave theory in a fashion similar to that for velocity (see, for example,
Denny, 1988). However, these
accelerations are small relative to those in broken waves (typically less than
5 m s-2), and their effects will not be explored here.
Although the orbital velocities imposed by unbroken waves dominate flow
outside the surf zone, unidirectional currents can also be present, and these
may affect algal dynamics. Two types of current are worthy of note. Subtle
aspects of wave motion result in a slow transport of water in the direction of
wave propagation (i.e. typically towards shore). This current (which usually
amounts to at most a few cm s-1) is known as Stokes drift
(Kinsman, 1965;
Denny, 1988
). In addition, a
number of oceanographic factors can result in a longshore current
(Pond and Pickard, 1983
). The
speed of this current can vary widely over time and as a function of location,
but is generally slow compared with orbital velocities.
Flow after wave breaking
Thus far, we have considered only the regular, predictable flows associated
with currents and unbroken waves. These are the flows imposed on the giant
kelps. However, as waves move inshore, become unstable and break, they
degenerate quickly to produce the complex, highly energetic turbulence
characteristic of a propagating bore, the type of flow imposed on algae in the
surf zone. The rotating, stretching and twisting eddies associated with this
complexity combine with the bulk movement of the bore itself to generate
maximal flow speeds somewhat in excess of
(gHb)1/2
(Denny, 1995;
Gaylord, 1999
), where
g is the acceleration due to gravity and Hb is
the height of the bore. As an example, a typical broken wave with an inshore
height of 2 m will produce velocities somewhat in excess of 4.4 m
s-1, more than double that found in an unbroken wave of the same
height. Topographic effects may then further funnel the flow locally to create
the exceptionally large velocities (25 m s-1) noted in the
Introduction. Because there is only modest attenuation with vertical position
within a broken wave and little time for a boundary layer to be established,
these extreme surf-zone flows can impinge routinely even on algae whose blades
are situated only a few millimeters above the substratum.
The spatial scales over which velocity is uniform within a turbulent bore
range from a few centimeters to over a meter
(Gaylord, 2000). These spatial
scales are 1-2 orders of magnitude smaller than those associated with unbroken
waves, but are still large enough to encompass substantial portions of most
intertidal seaweeds. As a result, many moderately sized surf-zone plants will
experience velocities as largely coherent flow fields along their lengths.
This is not the case for the fluid accelerations produced in bores, which
are typically characterized by spatial scales of less than a centimeter
(Gaylord, 2000). The forces
imposed by these accelerating parcels of fluid vary in proportion to the
volume of organism they enclose. As a direct consequence, although the
magnitudes of the accelerations can be impressive (commonly hundreds of m
s-2) (Denny et al.,
1985
; Gaylord,
1999
), their small spatial scales prevent them from interacting
with a large enough portion of an alga to impose a dangerous force
(Gaylord, 2000
). This
hydrodynamic subtlety appears to negate a number of expectations, based on
standard fluid theories, that fail to account for the restricted dimensions of
the accelerations (e.g. Denny et al.,
1985
; Gaylord et al.,
1994
).
There is an additional fluid-dynamic phenomenon that occurs high in the
surf zone. When macroalgae are emergent at low tide, arriving waves may crash
directly against them. This leaves individuals with no interposed liquid
cushion for protection. Recent field measurements indicate that the most
severe forces applied to intertidal plants are often associated with such
`wave impingement' events (Gaylord,
2000; Gaylord et al.,
2001
). These large, but brief, forces arise intrinsically as a
result of the requisite rapid evolution of a far-from-steady-state flow field
as the free surface of a wave first encounters an organism
(Gaylord, 2000
).
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Flow and survival |
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![]() | (1) |
|
As noted previously, in the absence of flow, most nearshore algae are not
noticeably streamlined. However, as a result of the structural flexibility of
algal fronds, this impression can be misleading. In unidirectional flow,
fronds bend in response to the applied force, and the plant reorients and
rearranges passively in a manner that results in an overall streamlining
(Koehl, 1984,
1986
;
Koehl and Alberte, 1988
). As a
consequence, ß for wave-swept algae in flow is universally less than 2
(typically approximately 1.5), and values as low as 0.8-0.9 have been reported
(Carrington, 1990
;
Bell, 1999
;
Gaylord et al., 1994
;
Gaylord, 2000
). There seems to
be little correlation between the still-water shape of an alga and its inflow
value of either ß or C. In other words, the flexibility of algae
(due both to their basic body plan and to the compliance of their materials)
allows fluid-dynamic forces to be decoupled from shape in rapid,
steady flows many wave-swept algae seem to be approximately equally
streamlined.
Given this decoupling, the mechanical survival of a number of macroalgae
subjected to drag or impingement forces is primarily a function of the
interplay between maximum water velocity, frond area and the strength of
either the stipe or holdfast (see, for example,
Collado-Vides et al., 1998;
Kawamata, 2001
). For example,
Carrington (1990
) found that,
while the frond area of the high intertidal red alga Mastocarpus
papillatus increased throughout the plant's life, the stipe
cross-sectional area (and with it the stipe's strength) remained constant.
Setting F in equation 1 equal to the stipe's breaking strength,
Fbr, we can solve for the maximum frond area,
Amax, as a function of imposed velocity:
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The reproductive structures of M. papillatus are distributed over
the fronds and, as a result, the plant's reproductive output is approximately
proportional to frond area. Thus, because stipe strength is constant, the
reproductive output of plants in areas of high flow is likely to be less than
that in areas of low flow. The logic of this evolved life-history strategy
becomes apparent only when we note that in this species many stipes emerge
from a single, crustose holdfast. The strength of the stipes is low enough to
ensure that the fronds (which can regrow) will detach before the holdfast
(which is perennial) tears loose
(Carrington, 1990). In `good'
times (a growing season without extreme water velocities), the fronds can
reach a large size, and reproductive output is substantial; in `bad' times
(perhaps an early storm hits before spores can be released), the fronds (and
potentially the individual's entire reproductive output) may be lost, but the
holdfast persists to try again. These mechanics can lead to seasonal
oscillations in blade size (Denny and
Wethey, 2000
). In an analogous scenario, differential mortality
due to different scaling of blade area to stipe strength has been used to
explain the pattern of coexistence in two intertidal algal species in Maine
(Dudgeon and Johnson, 1992
).
Chondrus crispus outgrows its neighboring Mastocarpus
stellatus but, because it has larger blades for its holdfast strength, it
is preferentially weeded out by winter storms. In general, disparities between
applied hydrodynamic force and stipe or holdfast strength can be used to make
quantitative predictions regarding habitat, life history or distributional
patterns in algal species (e.g. Denny,
1995
; Shaughnessy et al.,
1996
; Carrington et al.,
2001
; Kawamata,
2001
).
Note that in some of these studies, however, calculations of applied
hydrodynamic force have employed values for ß based on measurements made
for u<5 m s-1 and, thus, represent extrapolation well
beyond the available data. Bell
(1999) discusses the potential
pitfalls of this extrapolation, but full resolution of the problem awaits drag
measurements at higher velocities.
In contrast to the Mastocarpus and Chondrus discussed
above, other species react to the imposition of dangerously high forces in a
fashion that preserves at least part of the fronds. Blanchette
(1997) has shown that, when
transplanted from an area of slow flow to an exposed shore, the rockweed
Fucus gardneri selectively `tatters'. The overall area of the frond
is reduced as distal sections break off, resulting in a `pruned' plant of a
size appropriate for its new environment.
Plant/flow relationships can also be modulated by other organisms. For
example, numerous studies have documented the roles of grazers in undermining
the structural integrity of macroalgal stipes (e.g. via fracture
arising from sea urchin bites) (Koehl and
Wainwright, 1977; DeWreede et
al., 1992
).
Interactions among multiple seaweed individuals in dense assemblages can
also affect flow forces. For example, fronds of C. crispus may
experience reduced forces as they recline against their neighbors
(Johnson, 2001). It is also
well recognized that individuals within a clump can `hide' in the wake of
upstream organisms (e.g. Eckman et al.,
1989
; Carrington,
1990
; Johnson,
2001
), employing an avoidance strategy similar to that used by
plants compressing into the lower-velocity regions of substratum interstices
(Koehl, 1984
,
1986
,
1999
). In more extensive algal
stands, even larger-scale flows may be diverted to pass around the periphery
of an assemblage or attenuated within its interior (e.g.
Fonseca et al., 1982
;
Jackson and Winant, 1983
;
Eckman, 1987
;
Gambi et al., 1990
;
Jackson, 1998
). In yet other
cases, propagating waves of deformation may pass through the canopy of
understory algae as they bend synchronously to align with flow
(Ackerman and Okubo, 1993
).
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Flexibility and dynamics |
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One of the more visible effects of reorientation is apparent in large
subtidal species (e.g. N. luetkeana and M. pyrifera) that
experience predominantly the simple flows of unbroken waves. These algae sway
back and forth as waves pass by but, because of their great length, may only
rarely be stretched out fully by a wave orbit before the flow reverses. This
strategy of `going with the flow' is therefore thought to result in a
reduction of applied force (Koehl,
1984,
1986
,
1999
). There are additional
complications, however, due to Stokes drift. Because this unidirectional
component of flow acts along the direction of wave propagation, it has the
potential to tug a plant to an extended position in which wave-driven
velocities would impose force unabated. In other words, no matter how long the
stipe, it has a limited time in which it can go with the Stokes flow (see also
Stevens et al., 2001
). The
critical issue then becomes whether a complementary longshore current is also
present. By rotating the axis along which a plant is extended to an
orientation more parallel with the coast, a longshore current may maintain an
alga in a slack position with respect to the onshore/offshore orbits of the
waves. In this way, a longshore current may ameliorate the tendency for Stokes
drift to move the plant into a vulnerable orientation.
Although a critical field examination of the efficacy of going with the
flow has not been conducted, there are some relevant data available for
evaluating it. Measurements of flow damping within kelp beds in Southern
California suggest, for example, that there is little attenuation of energy at
the frequencies of ocean waves (Elwany et
al., 1995). This finding supports the view that orbital velocities
often do not apply substantial forces to large canopy-forming species, since
otherwise the action of drag would result in a loss of this energy. Similarly,
field measurements of tensile force in the stipe of a large N.
luetkeana (Fig. 2B;
Denny et al., 1997
) showed
that when wave heights were approximately 1 m, forces were small (only
approximately 8 N in excess of buoyancy). Note that the strategy of going with
the flow is unlikely to function as effectively in intertidal regions where
bores often travel for tens of meters (many frond lengths) in the same
direction before flow reversals occur, although some data suggest modest
benefits (Koehl, 1999
). This
point, in conjunction with the augmented flow speeds found in the surf zone,
may contribute to the expected capacity of wave breaking to set inshore
boundaries to kelp beds (e.g. Seymour et
al., 1989
; Graham,
1997
).
As the above discussions of algal reconfiguration and reorientation have
indicated, there are a number of advantages to being flexible. However, there
may also be some negative ramifications. One potential disadvantage derives
from the momentum that seaweeds acquire as they move passively in flow.
Because an attached alga has a finite range of motion, the plant's own mass
can apply an `inertial force' to itself as it decelerates at its furthest
point of excursion (Denny et al.,
1998). Under some circumstances, the component of force associated
with momentum is predicted to outweigh any accompanying benefit due to going
with the flow (Denny et al.,
1997
; Gaylord and Denny,
1997
). Plants appear to be most vulnerable to this momentum effect
when their natural periods of motion are near the dominant period of the
arriving waves. This causes tuning between the external force and the dynamic
response of the seaweed and essentially creates a plant/flow analogue to the
socalled `resonance' phenomenon often observed in simple springmass systems
(Fig. 3;
Denny et al., 1998
). Other
models predict additional, unfurling behaviors in some algae (e.g. the
featherboa kelp Egregia menziesii) that may lead to superimposed
whiplash (Friedland and Denny,
1995
).
|
The fact that inertial forces due to momentum scale with mass may have
consequences regarding the size of wave-swept algae. As described above,
limits to the size of M. papillatus, M. stellatus and C.
crispus exist because the forces of drag or wave impingement
(proportional to frond area) increase out of proportion to stipe strength.
Large kelps (such as N. luetkeana), which go with the flow (and
thereby possibly avoid these forces), could be immune to this effect. However,
because factors that scale with mass are likely to increase more rapidly with
increases in size than are factors that scale with area, this sets up a
scenario in which, as a plant gets bigger, massdependent forces due to a
seaweed's momentum could eventually come to exceed its area-dependent strength
(Gaylord, 2000). This raises
the possibility that motion allowed by flexibility in seaweeds places upper
bounds on size (albeit less restrictive ones) even for the giant kelps.
Further research will be required on this topic, however, before it can be
viewed as anything other than conjecture.
Emerging evidence regarding the potential importance of wave impingement
has exposed other potential limits to the functionality of a flexible body
plan. Field recordings of impingement forces indicate that they last only a
small fraction of a second (often less than 0.1 s;
Fig. 2C)
(Gaylord, 2000;
Gaylord et al., 2001
). Thus,
for many seaweeds that reorient, the peak of such a force pulse may have
passed long before a plant can fully respond to it
(Koehl, 1986
;
Denny, 1987
;
Gaylord, 2000
). However, if an
alga is already aligned with the direction of an impingement pulse when it is
first applied, there may be a much reduced (or even nonexistent) capacity for
amelioration of the effects of the pulse
(Gaylord et al., 2001
).
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Future directions |
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Acknowledgments |
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