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First published online May 1, 2006
Journal of Experimental Biology 209, 1894-1903 (2006)
Published by The Company of Biologists 2006
doi: 10.1242/jeb.02225
The hydrodynamic effects of shape and size change during reconfiguration of a flexible macroalga
Department of Biological Sciences, University of Rhode Island, Kingston, RI 02881, USA
* Author for correspondence at present address: Hopkins Marine Station of Stanford University, Pacific Grove, CA 93950, USA (e-mail: boller{at}stanford.edu)
Accepted 21 March 2006
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Summary |
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2 m s–1.
Reconfiguration was due to two separate mechanisms: whole-alga realignment
(deflection of the stipe) at low velocities (<0.2 m s–1)
and compaction of the crown (reduction in frontal area and change in shape) at
higher velocities. Change in frontal area contributed more to drag reduction
than change in drag coefficient. Drag coefficient and frontal area both
decrease exponentially with increasing water velocity, and a mechanistic model
of drag was developed with explicit functions to describe these changes. The
model not only provides mechanistic parameters with which to compare
reconfiguration among individuals and species, but also allows for more
reliable predictions of drag at high, ecologically relevant water
velocities.
Key words: biomechanics, ecology, seaweed, Chondrus crispus
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; Menge, 1976;
Paine and Levin, 1981;
Denny, 1995;
Carrington, 2002). These forces
include the well-known lift and drag, and also the impingement force,
associated with the impact of a wave on an emerged object
(Gaylord, 2000). Sessile
organisms have adopted a variety of different strategies for surviving these
physical stressors (Denny et al.,
1985). Some, such as limpets and sea stars, are rigid and armored
while others, such as anemones and macroalgae, are flexible
(Koehl, 1977;
Vogel, 1994;
Denny, 1988). The dominant
hydrodynamic force imposed on macroalgae is likely drag
(Denny and Gaylord, 2002). The
impingement force may often exceed drag in the intertidal zone
(Gaylord, 2000), but has not
been extensively studied and is not addressed here.
For macroalgae, two mechanisms have been identified by which marine
macroalgae use flexibility to reduce drag. First, this hydrodynamic force may
be decreased in macroalgae by `going with the flow' and reducing the velocity
of the water relative to their blades
(Koehl, 1984;
Koehl, 1986;
Koehl, 1999;
Gaylord and Denny, 1997;
Denny et al., 1997;
Stewart, 2004). A second
mechanism is called reconfiguration, where the size and shape of the macroalga
changes with velocity to reduce drag
(Vogel, 1984;
Vogel, 1989;
Sheath and Hambrook, 1988;
Carrington, 1990;
Gaylord and Denny, 1997;
Johnson, 2001;
Pratt and Johnson, 2002;
Sand-Jensen, 2003;
Harder et al., 2004). For
macroalgae, the reduction in drag via reconfiguration is due to a
passive bending of the organism in response to the force
(Vogel, 1994).
In general, biologists define drag (FD) as:
 | (1) |
is the density of the fluid, U is the fluid velocity
relative to the organism, A is a characteristic area (size) of the
organism, and CD is the drag coefficient, a dimensionless
number that accounts for the interaction between the flow and the shape of the
object. In this equation, reconfiguration is not addressed because the size
and shape of the organism are assumed to be constant. However, the
relationship between drag and reconfiguration has been quantified as Vogel's
E, a measure of the difference between the squared relationship
between velocity and drag and the lower drag seen in reconfiguring organisms
(Vogel, 1994). Vogel's
E is easily calculated as the slope of the linear regression of the
log–log plot of speed-specific drag (F/U2)
versus fluid velocity (U). Values for Vogel's E
typically range from 0 to –2; more negative values imply increased
reconfiguration. Reconfiguration has been incorporated into Eqn 1 by modifying
the exponent of velocity by subtracting Vogel's E, resulting in the
equation:
 | (2) |
; Gaylord,
2000; Denny and Gaylord,
2002).
While Vogel's E is useful for quantifying reconfiguration and
comparing drag among organisms, its application is limited. First, it is an
indirect measure of reconfiguration. While it is the shape and size that
change with increasing water velocity, Vogel's E modifies the
exponent of the velocity only. Direct measurements of changes in shape and
area should be considered independently to understand the mechanisms of
reconfiguration. Second, the introduction of Vogel's E to the
exponent of velocity modifies the dimensionality of CD
(Denny and Wethey, 2001;
Sukhodolov, 2005) (but see
Sand-Jensen, 2005), which was
originally defined as a unitless parameter
(Vogel, 1994). Thus, drag
coefficients calculated for organisms with different Vogel's E have
different units, complicating their comparison. Third, Vogel's E
characterizes reconfiguration over the range of velocities for which it is
measured. It should not used to extrapolate drag at higher velocities, despite
its use for such a purpose in the literature
(Vogel, 1994).
While it is commonly accepted that reconfiguration can be of great
importance for reducing drag on macroalgae
(Denny and Gaylord, 2002;
Harder et al., 2004), the
mechanisms of reconfiguration, specifically how changes in area and shape
combine to reduce drag and the relative contributions of each mechanism to the
overall reconfiguration, are poorly understood. This study examined
reconfiguration of the red alga Chondrus crispus, a dominant space
holder in the New England rocky intertidal zone, to determine the mechanisms
of drag reduction via flexibility. The changes in algal size and
shape in flow were measured directly, allowing for a comparison of their
contributions to drag reduction. Further, these analyses allow for the
development of a new mechanistic model for drag on flexible organisms.
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17°C
seawater for up to 3 days. The holdfast of each individual was carefully
dissected from the rock and shaved with a razor blade to achieve a flat
surface that was then affixed to an acrylic mount using cyanoacrylate glue.
Life history phase was identified after hydrodynamic analyses using a
resorcinol test (Garbary and DeWreede,
1988) and only gametophytes were used in the study. The height
(±0.02 cm) and planform area Aplan (±0.0004
cm2) were measured using ImageJ software (ver. 1.33, National
Institutes of Health, Bethesda, MD, USA) from photographs of individuals
sandwiched between two sheets of acrylic.
Hydrodynamic characterization
The hydrodynamic performance of each individual was measured in seawater
using a medium-speed recirculating flume similar to those described by Denny
(Denny, 1988), but modified for
direct measurement of reconfiguration (Fig.
1). The flume consisted of a rectangular acrylic outer tank above
a PVC return pipe (0.2 m diameter, 0.031 m2 cross-sectional
area), supported by a custom-designed extruded aluminum frame (80/20 Inc.,
Columbia City, IN, USA). Within the rectangular tank, a choke reduced the
cross-sectional area to 0.0225 m2 in the 0.15 mx0.15
mx0.30 m (WxHxL) working section. A diffuser gradually
increased the cross-sectional area downstream of the working section. Turning
vanes mounted within each elbow of the return pipe and two sets of flow
straighteners (0.013 m square, 0.00016 m thick plastic grid) stabilized the
flow. Flow was generated by two 19 cm bronze propellers driven by a 1 HP
variable speed DC permanent magnet motor (PM9100TF, Boston Gear, Quincy, MA,
USA). The motor controller (RG500A, Minarik Corp., Glendale, CA, USA) was
interfaced with the analog output of an analog-to-digital converter
(DAS16/12-AO, Measurement Computing Corp., Middleboro, MA, USA), allowing
water velocity to be controlled by the data collection computer. Water
velocity (±0.2 m s–1) was calibrated to propeller
speed (r.p.m.) by following neutrally buoyant particles with a high-speed
digital video system (Motionscope PCI, Redlake, San Diego, CA, USA).
Hydrodynamic performance variables (i.e. drag, area, shape) were recorded
across velocities ranging from 0 to 2 m s–1 at 0.1
m s–1 intervals.
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Drag (±0.001 N) was measured on each individual using a 1 kg (9.8 N)
strain gage force transducer (FORT1000, WPI Inc., Sarasota, FL, USA). An
aluminum adapter connected the force transducer to the acrylic mount and
extended the moment arm to 10 cm. This extension decreased the maximum load to
2 N but increasing the sensitivity of the transducer. The force signal
was amplified by a transducer amplifier (TBM4, WPI Inc.) and calibrated by
hanging weights from the acrylic mount. A PC computer collected force data at
100 Hz for 25 s with the 12-bit analog-to-digital converter. Drag at each
velocity was calculated as the average of the 2500 points collected at each
velocity. The algae were positioned upside down in the tank to keep the force
transducer dry; while this posture may have influenced the alga's shape and
projected area of alga at very low velocities (<0.1 m
s–1), gravitational and buoyant forces were otherwise
negligible. Further references to the position and orientation of an alga
reflect the natural, upright perspective, despite the experimental
conditions.
To compare to previous studies, Vogel's E was calculated as the
slope of the log–log plot of speed-specific drag
(FD/U2) versus velocity
(Vogel, 1994). Due to the
broad range of water velocities examined and the differences between low
velocity and high velocity reconfiguration, E was determined for two
separate velocity ranges, 0–0.5 and 0.5–2.0 m s–1
(Vogel, 1994). Additionally,
planform area-based drag coefficients (CD,plan) were
calculated at 0.5 and 1.9 m s–1 (just below the maximum flow
of the tank) as:
 | (3) |
Reconfiguration was measured directly by using a two-camera high-speed digital video system to record the frontal (projected into the flow) and side views of each alga during flume runs (Fig. 1). The frontal images were obtained with a camera equipped with a 12–75 mm zoom lens pointed at an 11 cmx7 cm mirror rigidly suspended at a 45° angle in the downstream end of the diffuser (Fig. 1). Morphological data were quantified at each velocity using ImageJ software. Stipe angle, a measure of the overall posture of the alga, was defined as the angle of the stipe relative to the substrate (Fig. 2). Crown angle, a measure of the shape of the alga interacting with the flow, was defined as the angle formed by three points: the top (nearest the center of the tank) and bottom (adjacent to the wall) edges of the crown and the stipe crown junction (Fig. 2). Both stipe and crown angle were measured from the side view images.
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Frontal area at each velocity (AF) was measured from
the frontal view images by tracing the edge of the silhouette of the alga
manually in ImageJ, excluding large (>1 mm2) gaps within the
perimeter. AF was then normalized by a representative area
(Arep, the frontal area when the alga was reconfigured
such that the stipe was parallel to the flow at 0.2 m
s–1) to remove the variation in overall size among
individuals. TableCurve2D software (v4.07, Systat Software Inc., Point
Richmond, CA, USA) was used to determine the best simple consensus model (a
three-parameter exponential decay function) that described both individual and
pooled data for velocities above 0.2 m s–1 (where the alga
was oriented parallel with the flow). The normalized areas as a function of
velocity (aU) were then fit to the exponential decay
function:
 | (4) |
is the minimum normalized area of the alga
(maximum reconfiguration), aR is a coefficient describing
the magnitude of area reduced due to reconfiguration, and ßa
is the normalized area reconfiguration coefficient, a term that describes the
steepness of the decay function. The normalized area function parameters,
goodness of fit and 95% confidence intervals were determined for both
individuals and pooled data using TableCurve2D.
Velocity-specific drag coefficient was calculated using Eqn 3, where
A was AF measured directly at each specific
velocity (Vogel, 1994).
TableCurve2D was again used to determine the best simple model to describe the
change in drag coefficient for velocities above 0.2 m s–1 and
again an exponential decay function was chosen. The drag coefficient as a
function of water velocity (CU) was fit to the equation:
 | (5) |
is the minimum CD (at
maximum reconfiguration), CR is a coefficient describing
the magnitude of the reduction of CD due to
reconfiguration, and ßC is the reconfiguration coefficient for
CD. The CU function parameters and 95%
confidence intervals were determined using TableCurve2D for velocities above
0.2 m s–1 (where the alga was oriented parallel with the
flow).
Additional parameters, the critical velocities for area reconfiguration
(Ucrit,a) and for CD reconfiguration
(Ucrit,C), were defined to express the water velocity at
which reconfiguration approached its maximum effect. A threshold of within 5%
of the asymptote value of Eqn 4 and 5 was chosen to represent this velocity.
Because the value is approached from above, this corresponds to a value of
105% of the asymptote, thus Ucrit,a was calculated by
replacing aU with (1.05a) and
solving for U in Eqn 4. Ucrit,C was calculated in
an analogous manner. Critical values were calculated for both individual and
pooled data. It should be noted that a threshold of less than 5% could have
been chosen, resulting in higher Ucrit values that were
closer to the asymptote. However, lowering the threshold would result in much
higher Ucrit values with little corresponding change in
the aU or CU because of the
exponential decay.
A new model for reconfiguration
A model for drag on reconfiguring macroalgae was defined by replacing
A and CD in Eqn 1 with the pooled functions
describing the Chondrus' change in area and CD
with velocity, aU and CU,
respectively. Because aU described the change in
normalized area, the equation was multiplied by Arep to
describe the force on an individual, such that the mechanistic model of drag
with reconfiguration (FDR) was defined as:
 | (6) |
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Drag was variable among individuals, with FD ranging from 0.28 to 1.48 N at 1.9 m s–1 (Fig. 3). Reconfiguration, as quantified by Vogel's E, ranged from –0.35 to –0.85 for low water velocity and –0.44 to –0.81 for high velocity (Table 1). CD,plan calculated at 0.5 m s–1 ranged from 0.33 to 0.92, but was lower (0.15 to 0.46) when calculated at 1.9 m s–1. The mean percent errors from the measured force were 56% for low velocity predictions and 21% for high velocity predictions (Table 1). Paired t-tests indicated significant deviation from the actual value for both low (t=–8.41, d.f.=18, P<0.01) and high (t=9.77, d.f.=18, P<0.01) velocity predictions.
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Stipe angles were initially high (near 90°) in still water and dropped dramatically over low velocities, as the alga came in contact with the wall of the tank (between 0.1 and 0.2 m s–1, Fig. 4). Once substrate contact was made, the stipe was held off the wall by the crown, and only gradual decreases in angle were observed as the crown compressed. Crown angles were more variable than stipe angles, with changes in the position of branches causing fluctuations at low water velocities (<0.5 m s–1). Angles generally decreased as velocity increased, indicating compaction of the crown (Fig. 5).
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Frontal area generally decreased with water velocity for all individuals
(Fig. 6). Note that
AF often increased at extremely low velocities (<0.1 m
s–1) as the posture of the alga changed from upright to
parallel with the flow. Eqn 4 described aU well for water
velocities above 0.2 m s–1 (all P<0.01;
R2=0.96–0.99), with parameter ranges of:
a=0.32–0.56,
aR=0.66–0.89, and ßa=0.49 to 1.30 m
s–1 (Table 2).
The fit of pooled data was also well described by Eqn 4 (P<0.01,
R2=0.89) and were very similar to the means of individual
fits. Pooled parameters (±95% confidence intervals) were estimated as:
a=0.44±0.02,
aR=0.75±0.03, and
ßa=0.70±0.08 m s–1
(Fig. 7). Individual
Ucrit,a ranged from 1.64 to 4.94 m s–1
and averaged 2.55 m s–1
(Table 2). The pooled
Ucrit,a was 2.47 m s–1.
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Drag coefficient decreased with increasing water velocity, ranging from
1.02 to 1.57 at 0.2 m s–1 and 0.56 to 0.92 at 2.0 m
s–1 (Fig. 8).
Eqn 5 described CD well for water velocities above 0.2 m
s–1 (all P<0.01;
R2=0.91–0.99) with parameter ranges of
C=0.55–96,
CR=0.64–1.68 and ßC=0.24–0.85
m s–1 (Table
2). When pooled among individuals, the CU
model yielded parameters (±95% confidence intervals) of
C=0.75±0.03,
CR=0.87±0.12 and
ßC=0.42±0.08 m s–1
(P<0.01; R2=0.59;
Fig. 8). Again, pooled
parameter values were very similar to the means of individual parameters. Drag
coefficient was also correlated with the shape of the crown at low to
intermediate velocities (0.2–0.7 m s–1). In general,
CD values increased with crown angle (mean slope=0.016,
mean R2=0.70), such that broader crowns had higher
CD values (Fig.
9). Individual Ucrit,C ranged from 0.79 to
2.72 m s–1 and averaged 1.56 m s–1
(Table 2). The pooled
Ucrit,C was 1.32 m s–1.
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Low versus high velocity reconfiguration
Two distinct processes of reconfiguration are evident in this study,
supporting the idea that reconfiguration across broad ranges of fluid velocity
may have different mechanisms and should not necessarily be examined as a
single process (Vogel, 1994).
First, at low water velocities (<0.2 m s–1,
Fig. 4), reconfiguration is
dominated by the deflection of the stipe. This `realignment' changes the
posture of the macroalga from an upright (tree-like) shape to one where the
stipe is bent parallel to the flow and the overall shape is similar to a cone
tethered at its peak. This realignment of the stipe causes it to be loaded in
tension, rather than in bending, and should result in overall lower stresses
compared to bending (Koehl,
1979). The second process of reconfiguration occurs at higher
water velocities, as the crown of the alga `compacts' and causes a gradual
change in the shape (crown angle) and size (AF)
interacting with the flow (Figs
5,
6). Thus, compaction effects
changes in size and shape, but not the overall posture of the alga. The
different velocity ranges over which these two mechanisms of reconfiguration
act highlight the pitfalls in applying low-velocity hydrodynamic data to
high-velocity field conditions (Bell,
1999; Denny and Gaylord,
2002).
The two distinct mechanisms for reconfiguration have different ecological
implications. Realignment in response to the oscillatory flow typical of the
intertidal zone (Denny, 1988)
may increase photosynthetic rates by allowing alternate sides of the alga to
be exposed to light. Such posture changes may also reduce self shading
(Koehl and Alberte, 1988) and
light competition among individuals in an algal canopy
(Greene and Gerard, 1990;
Kübler and Raven, 1994).
At higher velocities, where forces approach those required to dislodge
individuals in the field (Carrington et
al., 2001), greater compression results in lower drag. Thus
greater reconfiguration by this mechanism should improve survival at higher
water velocities and the preservation of photosynthetic and reproductive
tissues. However, photosynthetic rates are reduced in small macroalgae across
this velocity range (Stewart and
Carpenter, 2003), suggesting that crown compression can negatively
influence photosynthesis due to the reduction in the presentation of
photosynthetic area to sunlight.
Frontal area
The two mechanisms of reconfiguration suggest that there should be little
correspondence between changes in area during realignment and compaction.
Realignment is effectively a change from a side view to the top view of the
alga, with respect to the flow. This change in posture accounts for the
unpredictable changes in frontal area at low velocities. During compaction,
the change in frontal area was remarkably smooth. Additionally, there was no
relationship between size (Aplan, Arep
or height) and proportion of area reduced; all individuals had relatively
similar proportional decreases in frontal area, as quantified by
a, despite the broad range in size and bushiness
among individuals. While bushier individuals might be expected to have more
potential for reconfiguration because of their three-dimensional structure,
and thus have a lower a, this was not the case in
Chondrus. Further study of other macroalga shapes is warranted.
Drag coefficient
The direct measurement of area projected into the flow also allows for the
calculation of drag coefficients that are comparable to those measured for
rigid objects (where CD is defined relative to frontal
area). Calculated in this way, drag coefficients for Chondrus are
similar to those of bluff bodies, i.e. non-streamlined, rigid objects with
CD>0.5 (Hoerner,
1965; Vogel,
1994). The results reported here are distinct from other
macroalgae studies in which CD is calculated with the
planform area. Because CD is inversely proportional to
area (Eqn 3) and the planform area is a fixed value that is much larger than
the reconfigured frontal area of a macroalga, the CD
values calculated using planform area are lower than values calculated using
the reconfigured frontal area. Thus, the low CD values
reported for reconfigured macroalgae, e.g. 0.02–0.36
(Carrington, 1990), incorporate
both changes in the frontal area and CD. These planform
area-calculated CD values of reconfigured macroalgae
should not be compared to those of rigid objects (see
Gaylord et al., 1994;
Sand-Jensen, 2003) because the
two CD values have been defined differently.
Drag coefficient did decrease across moderate water velocities,
corresponding to the change in the angle of the crown
(Fig. 9), such that the
hydrodynamic behavior of the alga is similar to rigid cones of variable shape
pointed into the flow (smaller angles resulted in lower
CD) (Hoerner,
1965). This suggests that changes in the shape of the macroalga at
these velocities do result in reduced drag. At higher velocities, when
CD approaches its asymptote, the effects of shape change
are greatly reduced, and the macroalga behaves more like a bluff body (high,
constant CD).
While the changes observed in drag coefficient in this study are in part
attributed to the change in shape of the alga, other factors may be involved.
For bluff, rigid bodies, drag coefficient is not constant across large ranges
in Reynolds number (Re) (Vogel,
1994), thus the change in CD observed here at
low velocities may in part be due to this relationship between
CD and Re. However, Re for these
macroalgae ranged from 15 000 to 150 000, a range similar to where
CD does not vary for bluff bodies
(Vogel, 1994). It is also
possible that the juxtaposition of the substrate to the reconfigured alga at
high velocity may influence drag through an interaction with the boundary
layer (Vogel, 1994). The flow
in the flume was turbulent, suggesting that high velocities extended very near
to the substrate (Denny, 1988).
Carrington measured velocities in a similar flume that were 70% of the
free stream flow within 2 mm from the substrate at a free stream velocity
of 1.18 m s–1 (Carrington,
1990). Because even small reconfigured Chondrus extend
over 1.5 cm above the wall of the flume during maximum reconfiguration, they
cannot completely hide in the boundary layer and any effect is likely small.
Additionally, reconfiguration may reduce the surface area over which skin drag
can occur as the flume wall shelters one side of the alga from interacting
with the flow (Koehl, 1984).
However, this form of drag reduction may be most applicable to blade-like
species.
Shape or size
The relative contributions of area and drag coefficient to reconfiguration
change with water velocity. At low to intermediate velocities, both area and
CD decrease, suggesting that both are contributing to drag
reduction (Figs 7,
8).Between the
Ucrit,C and Ucrit,a (1.32 and 2.47 m
s–1), the change in area continues while
CD has effectively reached its asymptote. Within this
range, the change in area is largely responsible for drag reduction. Above
both critical velocities (>2.5 m s–1) both variables are
predicted to be constant such that these flexible organisms behave like rigid,
bluff bodies. These observations provide a mechanistic explanation to support
the model proposed (Bell,
1999), where the effects of reconfiguration were limited to low
velocities. Further study of drag and reconfiguration at the higher velocities
seen in the field (>10 m s–1)
(O'Donnell, 2006) is needed to
verify this hypothesis.
Should reconfiguration be considered a streamlining mechanism? In an engineering sense, streamlining is typically considered to be a process that results in reduced drag coefficient, but the term can also refer to any process that reduces drag. Algal reconfiguration does indeed reduce drag and, in a broader sense, can be considered a `streamlining' process. It is important to note that this streamlining is accomplished mostly by reducing frontal area, not drag coefficient. However, while reconfiguration effects some reduction in CD, the values calculated here are similar to those of bluff bodies. Thus these macroalgae do not form shapes that are `streamlined'.
Reconfiguration drag model
The reconfiguration drag model (Eqn 6) proposed here uses measured
relationships between water velocity and both frontal area and drag
coefficient to predict drag. The pooled parameters describing the change in
area and CD using Eqn 4 and 5, respectively, are
representative of the population of Chondrus examined in the study
and are meant to broadly describe the hydrodynamic performance of the
Chondrus morphologies found in the wave-swept intertidal zone. Thus,
the pooled parameters include error due to the morphological variation among
individuals and are probably best applied at a population level, not an
individual level. Nonetheless, the pooled model predictions for individuals
are all within 0.4 N at 2.0 m s–1
(Table 1). Examination of
individual variation would necessitate comparisons of the model fit to
individuals' data.
The use of a mechanistic model for drag generation on a flexible organism
improves our ability to predict drag at higher, ecologically relevant water
velocities. Due to the complexity of drag generation and the variety of
mechanisms that can contribute to reconfiguration, it has been unclear how to
extrapolate low velocity patterns to the velocities that would produce large
enough forces to damage and remove individuals
(Bell, 1999). This problem is
exacerbated by the fact that most studies of reconfiguration are limited to
low water velocities (<1.0 m s–1), due to the limitations
of flume design, and the difficulty of directly measuring drag in the field.
In this study, predictions of drag using Vogel's E and the planform
area calculated at low and high velocities consistently overestimate and
underestimate drag at a higher velocity, respectively. Our proposed model had
a smaller but still significantly different deviation from the measured force.
However, the asymptotic decline in aU and
CU suggests that the macroalgae will behave more as bluff
bodies at high water velocity, allowing for more accurate extrapolation to
higher water velocities. For example, in this study,
Ucrit,a is extrapolated to be 2.47 m s–1,
and is calculated as 2.76 in another study with a larger range of velocities
(up to 3.0 m s–1) (M. L. Boller and E. Carrington, manuscript
submitted for publication). This suggests that medium velocity measurements
(in the range of 3 m s–1) may be sufficient to make drag
predictions for some macroalgae, precluding the need to make difficult
high-velocity drag measurements. However, high velocity tests of this model
are needed.
The reconfiguration drag model also provides variables that can be used to
compare the hydrodynamic performance of macroalgal species and reconfiguring
marine invertebrates. Variation in Ucrit,a and
Ucrit,C among species represents differences in the rate
of reconfiguration relative to water velocity, while differences in
a and C are indicative
of variation in the absolute magnitude of reconfiguration. With these measures
of hydrodynamic performance, it may be possible to relate the effects of
morphological and material property variation to ecological performance.
The reconfiguration drag model (Eqn 6) may be considered more complicated
than the Vogel's E-corrected drag equation (Eqn 2) or others proposed
to describe drag on flexible organisms (e.g.
Gaylord, 2000;
Denny and Gaylord, 2002)
because of the addition of functions that describe area and
CD changes with velocity (Eqn 4 and 5). However, these
parameters are necessary to quantify the changes in the representative area
and CD because of the shape of the curve (an exponential
decay) and because the values do not asymptote to zero. However, the proposed
model could be considered less complicated because it preserves the standard
relationship between drag and flow velocity (i.e.
FD
U2)..
Conclusions
The reconfiguration of macroalgae is an unavoidable consequence of their
flexibility and an essential component for their strategy for survival in the
wave-swept rocky intertidal zone (Denny and
Gaylord, 2002; Harder et al.,
2004). This study clarifies the mechanisms by which
reconfiguration reduces drag: realignment and crown compaction. The latter
process reduces frontal area and drag coefficient of the macroalga by changing
the shape of the crown. These data reinforce the hypothesis that
reconfiguration is a dynamic process influenced by velocity-dependent
mechanisms (Vogel, 1994) and
suggests that reconfiguration in Chondrus is dominated by a change in
size of the macroalga and is less influenced by the interaction between the
macroalga's shape and the flow. The mechanistic model proposed here provides a
method of predicting drag on a flexible organism based on the predictable
changes in area and CD with water velocity. Because it is
based on the mechanisms underlying reconfiguration, it improves our ability to
predict drag on flexible organisms at high, ecologically relevant water
velocities above the limits of a flume. Most importantly, it provides a
framework to (1) compare the hydrodynamic performance among flexible organisms
and (2) investigate physical characteristics of the organisms that may
influence their hydrodynamic and ecological performances.
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List of symbols |
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TOPSummaryIntroductionMaterials and methodsResultsDiscussionList of symbolsReferences |
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Acknowledgments |
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Present address: Department of Biology, University of Washington, Friday
Harbor Laboratories, Friday Harbor, WA 98250, USA 
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References |
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TOPSummaryIntroductionMaterials and methodsResultsDiscussionList of symbolsReferences |
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