Kinematics of plaice, Pleuronectes platessa, and cod, Gadus morhua, swimming near the bottom
School of Natural Resources and Environment and Department of Ecology and Evolutionary Biology, University of Michigan, Ann Arbor, MI 48109-1119, USA
* e-mail: pwebb{at}umich.edu
Accepted 24 April 2002
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Summary |
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Key words: kinematics, plaice, Pleuronectes platessa, cod, Gadus morhua, swimming, power, tailbeat amplitude
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Introduction |
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The swimming kinematics of highly flattened benthic fishes differs from
that of their more fusiform relatives. The amplitude of body motions tends to
be large over a greater portion of the propulsor, with plaice being more
anguilliform and rays giving their name to swimming with large-amplitude
undulations of the pectoral fins in the rajiform mode
(Breder, 1926;
Rosenberger, 2001
).
Human-engineered vehicles and animals moving close to a solid surface can
reduce thrust requirements and increase efficiency as a result of interactions
between the wake and the surface (ground effect)
(Reid, 1932
; Blake,
1979
,
1983a
,b
;
Lighthill, 1979
;
Webb, 1993
). This hydrodynamic
ground effect does not affect fast-start performance
(Webb, 1981
), but continuous
swimmers do benefit (Blake,
1979
; Webb, 1993
).
The ground effect for axial undulatory swimming fish decreases rapidly with
height, being reduced by up to 95% at a gap/span ratio of 1, and becoming very
small, essentially negligible, at a value of 2
(Webb, 1993
). For rigid
bodies, ground effects reach zero at a gap/span ratio of 3
(Reid, 1932
; Blake,
1979
,
1983b
;
Lighthill, 1979
).
To assess the effects of a nearby surface on the swimming of benthic fishes, observations were made on plaice (Pleuronectes platessa) and cod (Gadus morhua) swimming at various heights above the bottom. This study focuses on plaice, a benthic species with a compressed body that swims on its side with propulsive motions normal to the substratum. As a result, plaice could derive substantial advantage from the ground effect, and swimming motions, especially tailbeat frequency, were expected to vary with height. Observations were also made on cod. Cod is a benthopelagic species that swims with a vertical posture, making swimming movements parallel to the substratum. Cod would be expected to derive little benefit from swimming near the bottom, so that swimming kinematics should be unaffected by swimming height above the bottom. Cod-like swimmers have been extensively studied and are included as a check that changes in the swimming motions of plaice at various heights above the substratum can be attributed to ground effects.
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Materials and methods |
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Apparatus
Swimming kinematics was observed in a flume described in detail by Arnold
(1969). Briefly, the flume was
constructed from 1.25 cm thick Perspex. It was approximately 6 m long, with a
0.3 mx0.3 m cross section. Water entered via a contraction
cone. The first 1.8 m of the flume was an entry section, which was followed by
an 1.8 m observation section. Nylon mesh screens delineated the observation
section. A clear Plexiglas boat floated on the surface, 1 cm below the wall
height, to eliminate surface waves. Cross-sectional flow profiles through the
observation section have been shown to be rectilinear
(Arnold, 1969
;
Webb, 1989
). The final 1.8 m
of the flume terminated at a gate. The height of the gate and the rate of
water input upstream of the contraction cone were used to regulate flow
velocity while keeping the water at the desired level. Free-stream flow
velocity was continuously monitored using a MINFLOW meter 15 cm above the
bottom immediately upstream of the observation section.
Swimming kinematics were recorded for fish swimming on the smooth bottom and over a grid of wires parallel to the flow lifting fish to heights, h, of 10, 50 and 100 mm above the bottom. The wires were strung on an aluminum frame with sides 1.0 cm square and 2 m long, with streamlined cross-pieces 0.624 cm thick at each end. Stainless-steel wires (0.01 mm diameter) were strung at 1.0 cm intervals along the cross-pieces and held under tension by turnbuckles at the downstream end of the grid. The frame for the grid extended beyond the end of the observation section, and the turnbuckles were beyond the downstream screen.
Swimming on a grid is not identical to swimming in the free stream at the
same height because the wires cause some retardation of flow across the
surface. Wires were spaced at the maximum distance that prevented fish from
passing easily through the grid. Actual downwash velocities are not known but,
because much of the mass of plaice is supported by buoyancy in water, they are
probably not large. A grid of wires with the same spacing normal to the flow
in the flume showed a velocity loss at 5 cm s-1 of less than 4%.
Maximum streamwise velocity losses due to such a grid at higher flow rates
were previously found to be up to 20%
(Webb, 1989).
Gap/span ratio
Pleuronectiformes swim on their side. As a result, body and caudal fin
motions are parallel to the ground. Therefore, thrust should be enhanced and
rates of working reduced by the ground effect
(Reid, 1932;
Lighthill, 1979
). Ground
effects depend on the gap/span ratio, z/B, where z is the
gap, the space between a solid surface and the thrust-producing body and fins,
and B is span, equal to the depth of the body and fins for plaice and
cod.
Fish propel themselves with flapping propulsors so that the gap varies
through a propulsor cycle. The ground effect decreases monotonically to an
asymptote with increasing z/B. To take into account this non-linear
variation, Webb (1993) used
the geometric mean gap for fish swimming near walls. This mean was calculated
from limits when a propulsive element was closest and most distant from a
solid surface. For the present experiments, this leads to:
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In addition, the ground effect is small at z/B2 for axial
undulatory swimmers and falls to zero at z/B of 3 for rigid bodies
(Reid, 1932
; Blake,
1979
,
1983b
;
Lighthill, 1979
). Values for
z were used only when z/B between the propulsor and a solid
surface was
3, with the exponent of equation 1 reduced accordingly.
The tail contacts the grid or bottom once in each tailbeat cycle. At this point, z1,bottom=h. At the other extreme of the tailbeat amplitude, z2,bottom=h+H, where H is the amplitude of a beat. For the special case of h=0, z1,bottom is zero and mean zbottom=H0.5. The total depth available was limited to 29 cm, so that z1,boat=29-h, and z2,boat=29-h-H, with the units being in centimeters.
Gap/span ratio was calculated similarly for cod, with distances to the walls replacing the distance to the bottom and the boat.
Experimental procedure
Individual fish were placed in the observation section and left overnight
at a free-stream velocity of approximately 5 cm s-1. The following
morning, the flow velocity was increased in increments of approximately 5 cm
s-1 (u) every 10 min (
t). An
experiment was terminated when a fish was unable to swim off the downstream
screen delineating the observation section. This 10-min critical swimming
speed (ucrit) was calculated as described by Brett
(1964
): 10-min
ucrit=up+
ut/
t,
where up is the penultimate speed before failure at which
fish swam for the full 10 min. The test temperature was 15°C.
At the end of an experiment, fish were killed with 3 ml l-1 phenoxyethanol. Mass was measured to within 1 mg in air. Each fish was also weighed in sea water (density 1.025 g cm-3), from which the density of each fish was calculated. Fish were suspended by a thread from a beam attached to the balance pan. The fish was immersed in a bucket of sea water. Measured weight was corrected for the weight of the beam and thread. Total length was measured to within 0.1 cm. These measurements are summarized in Table 1. The maximum or potential depth of the body and extended fins was measured to within 0.1 cm at 22 points equidistant along the centerline of cod and at 13 points along that of plaice. Fewer data points were required to characterize the simple body shape of plaice.
|
Throughout each experiment, fish were videotaped simultaneously in the horizontal plane and in the vertical plane via a mirror placed at 45° above the observation section. Sequences were analyzed that fulfilled the following conditions: (i) swimming was steady, defined as less than 10%, usually less than 5%, variation in speed between tailbeats, (ii) fish swam in the center of the flume, defined as the distances to each wall at the limits of tailbeat amplitudes varying by less than 10%, usually less than 5%, and (iii) for at least 10 complete tailbeats. Videotape was analyzed field-by-field (50 Hz), and body outlines were digitized through a tailbeat cycle. Tailbeat frequency was determined from the period taken by the tail to move from one extreme lateral position and back to the original position. The period was also measured for each half-beat. Tailbeat amplitude was measured as the distance between the maximum lateral displacements of the tip of the tail during a complete tailbeat and a half-tailbeat. The span of the trailing edges of cod was measured (i) at the tail, (ii) at the second dorsal and first ventral fin and (iii) at the third dorsal fin/second ventral fin, and for plaice (i) at the tail and (ii) at the maximum span of the body and median fins. The posterior speed of the propulsive wave was measured from successive positions of wave crests travelling along the body. The length of the propulsive wave was determined by dividing this wave speed by the tailbeat frequency.
The angle subtended by the body and the horizontal plane is the tilt angle
(He and Wardle, 1986;
Webb, 1993
). The midline along
the body of the swimming fish was determined as the central point between body
outlines at maximum amplitude. Digitized outlines were superimposed, and a
linear regression was fitted to amplitude limits along the body. The tilt
angle was measured as the slope of this line.
Statistical analyses
Multiple comparisons among various swimming parameters were compared using
analysis of variance (ANOVA) followed by Tukey's multiple-comparison tests to
locate significant differences. Relationships between kinematic parameters and
speed were examined using best-fit linear regressions. Comparisons between
pairs of data sets were made using Student's t-tests. Computations
were made using SYSTAT (Wilkinson,
1987). Significant differences are declared for
0.05.
Descriptive statistics are reported as means ± 2 S.E.M. (see
Sokal, 1995
).
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Results |
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The 10-min ucrit of cod was 57 cm s-1,
similar to that of 54 cm s-1 for plaice swimming at the bottom
(t-test, P>0.8). The 10-min ucrit of
plaice was unaffected by height for h10 mm, averaging 46 cm
s-1 (ANOVA, P<0.08). The mean 10-min
ucrit of these fish was significantly lower than that for
plaice swimming at the bottom (t-test, P<0.04).
Swimming mode
Both species swam by passing an undulatory wave along the body
(Fig. 2). The wavelength of the
propulsive wave, , was independent of both speed and swimming height
(ANOVA, P>0.9). Wavelengths averaged 16.4±0.2 cm
(N=259) (0.74L, where L is fish total length) for
plaice and 23.3±5.7 cm (N=158) (0.93L) for cod.
Plaice swimming was therefore more anguilliform than that of cod.
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Specific amplitude (H/L) of cod varied along the body length (Figs
2,
3A), as described for other
subcarangiform swimmers (Bainbridge,
1963; Webb, 1988
,
1992
). Values decreased
rostrally from a maximum of 0.16L at the trailing edge to a minimum
of 0.03L at a distance of approximately 0.3L from the nose.
Specific amplitude then increased over the head to 0.04L at the
nose.
|
The distribution of specific amplitude along the body length of plaice
differed from that of cod. Plaice specific amplitudes decreased continuously
from a maximum at the trailing edge to a minimum at the nose
(Fig. 3B). This pattern,
lacking a minimum behind the head, has been described for eel Anguilla
anguilla (Gray, 1933) and
tiger musky Esox sp. (Webb,
1988
) in association with a more anguilliform mode of
swimming.
In addition, specific amplitude increased at a lower rate over the
posterior of the body of plaice compared with cod (Figs
2,
3A,B). This is characteristic
of more anguilliform species compared with more carangiform species
(Breder, 1926).
The weight of cod in water, averaging 0.15 g, was 0.1% of the weight in air
(Table 1). Thus, cod were
essentially neutrally buoyant, and these fish swam with a horizontal posture
at all speeds and at all heights. Plaice were more dense than sea water,
supporting a weight of 4g, approximately 4.4% of the weight in air
(Table 1). There were no
significant differences in the duration or amplitude of tailbeats towards and
away from the bottom at any value of h (ANOVA, P>0.1).
However, plaice swam at positive tilt angles, as shown by the head-up postures
of the plaice centerline tracings in Fig.
2. These angles were variable, as observed elsewhere
(He and Wardle, 1986;
Webb, 1993
; Wilga and Lauder,
1999
,
2000
,
2001
). Although there was a
tendency for angles to decrease with increasing speed, the trend was not
significant; in addition, no relationship was found between tilt angles and
h (ANOVA, P>0.4). The overall tilt angle was
4±3° (N=259), and the 95% confidence interval around the
mean did not include zero.
Kinematics
Tailbeat frequency, F, and tailbeat amplitude, H, of cod
were not affected by swimming height above the bottom (ANOVA,
P>0.1). Data for fish swimming at various values of h
were therefore pooled (Fig.
4A). F increased linearly with speed from approximately
1.8 Hz at 10 cm s-1 to 3.9 Hz at 55 cm s-1. H
also increased linearly with speed from 2.9 to 4.7 cm (0.12 and
0.19L, respectively) over the same range of speeds so that
H=(2.5±0.2)+(0.039±0.007)u,
r2=0.55, P<0.001. These motions are comparable
with those of other species swimming in the water column when tailbeat
frequency is the major kinematic variable modulated with swimming speed.
Amplitude also increases with speed for some species, but not others
(Webb, 1975;
Videler, 1993
;
Webber et al., 2001
).
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For plaice, F for fish swimming at the bottom increased with speed from an average of 3.5 Hz at 25 cm s-1 to 4.7 Hz at 55 cm s-1 (Fig. 4A). At h=10 mm, there was some tendency for F to increase with speed, but the relationship was not significant (P=0.051). Therefore, F was independent of swimming speed, averaging 4.6, 6.0 and 5.8 Hz at 10, 50 and 100 mm respectively (Fig. 4B). The tailbeat frequencies of plaice swimming above the bottom at all speeds were significantly greater than those of cod (ANOVA, P<0.01).
The tailbeat amplitudes of plaice (Fig.
4C) were independent of swimming speed at all heights
(P>0.2). However, H was smallest at 1.5 cm
(0.07L) for plaice swimming at the bottom, compared with amplitudes
of 2.4-2.6 cm (0.11-0.12L) at h10 mm
(Fig. 4C). The tailbeat
amplitudes of plaice swimming at h
10 mm were not significantly
different from each other (P>0.3) but were significantly greater
than for plaice swimming at the bottom (P<0.001).
For plaice, amplitude distribution along the body was affected by
h (Figs 2,
3B). Specific amplitudes of the
body over the anterior 0.7L of the body of plaice were independent of
h, and those over the posterior 30 % differed for fish at 0 and
10 mm (ANOVA, P>0.2). The amplitudes at 10, 50 and 100 mm were
significantly larger than those at 0 mm (P<0.05). For example, the
tail amplitude averaged 0.07L for plaice swimming at the bottom and
0.11L for plaice swimming at 50 mm.
Span
The potential span, expressed as specific span, B/L
(Fig. 3C,D), varied with
position along the length of the body of both species. Variations for cod
followed the locations of the median fins
(Fig. 3C). The maximum span of
0.28L for cod occurred at 0.5L along the body, associated
with the second dorsal and first ventral fin. The maximum span exceeded that
of the third dorsal fin/second ventral fin of 0.2L at 0.75L
along the body, which in turn exceeded the maximum span at the caudal fin of
0.16L. As a result, upstream median fins could shed an outboard
portion of the vortex sheet which will not be absorbed at the leading edge of
the downstream fins. Such fins could contribute to mean thrust production
(Lighthill, 1975).
For plaice, the maximum specific span of 0.55L occurred at 0.45L from the nose (Fig. 3D). Span initially decreased continuously from this maximum over the posterior of the body, before increasing to 0.25L at the caudal fin. The trailing edge of the caudal fin was convex so that the maximum tail span occurred at approximately 0.1L anterior to tip of the caudal fin.
Swimming tail spans, B, of cod and plaice were independent of speed and swimming height (Fig. 4E) (ANOVA, P>0.09). Overall mean tail span was 3.9±0.1 cm (N=257) (0.16L) for cod, representing 89 % of the potential depth. For plaice, swimming tail span averaged 5.2±0.1 cm (N=158) (0.24L), which was not significantly different from the potential span. Although plaice had a smaller total length than cod, the tail spans of plaice were significantly larger (t-tests, P<0.01) than those of cod. Similar results were obtained for spans at other body locations, although these tended to be more variable that for the tail, especially for cod. Thus, the maximum span for cod averaged 90±23 % of the potential span (Fig. 3C) at the second dorsal/first ventral fin, and 85±21 % at the trailing edge of the third dorsal fin/second ventral fin. In contrast, the maximum span of swimming plaice was 98±10 % of the specific span (Fig. 3D).
Gap/span ratio
The span of propulsive sections of plaice did not vary with swimming speed.
Gap/span ratios at a given position along the body were therefore independent
of speed.
Cod were videotaped when swimming in the center of the flume. For all
points along the body, z/B>2; at this value of z/B,
ground effects are very small for axial undulatory swimmers
(Webb, 1993). Therefore
ground-effect interactions with the walls were considered negligible.
For plaice, z/B for the tail (ztail/B) was varied from 0.23 at the bottom to 2.16 at h=100 mm (Table 2). At the position of maximum span, z/Bmax was smaller, varying from 0.04 to 1 over the same range of h.
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Discussion |
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As with cod, the trailing-edge span and propulsive wavelength of plaice
were independent of speed. Tailbeat amplitudes of plaice were also independent
of speed; such speed-independence is common among carangiform and
subcarangiform swimmers (Webb,
1975; Videler,
1993
; Webber et al.,
2001
). Relationships between tailbeat frequency and swimming speed
of plaice were notably different from those of most swimmers. F
increased with speed, as is typical of other fish, only when plaice were
swimming at the bottom. For h
10 mm, F was independent of
speed.
Power
Interactions with the bottom by plaice are expected to affect rates of
working, with substantial reductions as z/B decreases below 2
(Webb, 1993). Therefore, to
evaluate better the effects of speed and height on swimming, rates of working
were determined using a bulk-momentum hydromechanical model derived from
elongated slender-body theory (Lighthill,
1975
; Wu, 1977
).
The mean rate of working for an element, x, along the body,
PX, is:
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Momentum carried by upstream fins and sharp body edges may be absorbed into
the wake of a re-entrant downstream fin with no net effect on the mean rate of
working, P. However, when the span of a body/fin element is greater
than that of a downstream en-entrant fin, the non-re-entrant portion of the
vortex sheet shed by the upstream fin contributes directly to P
(Lighthill, 1975;
Newman and Wu, 1973
;
Wu, 1977
). Both cod and plaice
have upstream fins with substantially larger spans than downstream fins.
Therefore, for cod, P was calculated as the sum of
PX for the non-re-entrant portions of the second
dorsal/first ventral fins, for the third dorsal/second ventral fins and for
the tail (Webb, 1988
,
1992
).
Plaice lack discrete upstream fins. The contribution of the continuous non-re-entrant portion of the dorsal and anal fins was calculated for 1-cm long panels along the body length from Bmax at 0.45L measured from the nose until body and fin span equaled the tail span at 0.7L (Fig. 3D). The non-re-entrant contributions from these sections were summed with the contribution from the tail to obtain P.
Swimming power, speed and kinematics
The swimming power for cod increased exponentially with swimming speed
(Fig. 5), as described for
other fishes swimming in the water column
(Webb, 1975;
Blake, 1983a
;
Videler, 1993
). The swimming
power of plaice at the bottom also increased with speed, but at lower rates
than for cod (Fig. 5). Plaice
at the bottom started swimming at a current speed of 25 cm s-1 and
cruised up to 54 cm s-1. At the lower end of this speed range,
P was slightly larger than for cod
(Fig. 5), but above 35 cm
s-1, plaice expended less mechanical power than cod. As h
increased, so did P. For plaice swimming at h
10 mm,
P was larger than that of cod over the whole range of cruising
speeds. Thus, the mechanical power expended by plaice for continuous cruising
was only comparable with that of cod when the plaice swam close to the
bottom.
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Part of the swimming power of plaice, the induced power, is used to
generate lift and to support the weight of the fish in water. In birds, the
necessity of supporting weight is associated with complex and asymmetrical
wing motions on the upstroke and the downstroke
(Norberg, 1990). No beat
asymmetry was detectable in plaice. Another approach to balancing weight is to
tilt, i.e. to swim or fly `uphill'. Negatively buoyant fishes swim at low
speeds with a positive, head-up tilt, as observed for plaice
(He and Wardle, 1986
; Wilga
and Lauder, 1999
,
2000
,
2001
).
Supporting weight dissipates energy as induced power
(Hoerner, 1975;
Anderson and Eberhardt, 2001
).
Because weight is independent of speed, a rapidly decreasing portion of the
total force generated by a propulsor is required to support the weight. As a
result, the associated induced drag decreases with speed. In the present
experiments, this might be expected to be associated with a decrease in tilt
angle with increasing speed, as observed for other fishes, but no significant
decreases were observed for plaice. This may occur because plaice do not swim
at the low speeds at which large changes in tilt angle occur. Thus, although a
decrease in tilt would be anticipated, this would be small and difficult to
identify given the usual variation in tilt angles
(He and Wardle, 1986
; Wilga
and Lauder, 1999
,
2000
,
2001
;
Webb, 2002
).
The effects of speed on induced power and that associated with
translocation may explain the relative constancy in kinematic variables with
speed of plaice swimming above the bottom. Kinematics and metabolic and
mechanical rates of working have recently been reviewed for negatively buoyant
swimmers, together with a thorough analysis of swimming for the brief squid
Lolliguncula brevis (Bartol et al.,
2001a,b
).
There is typically a shallow U-shaped relationship between power and speed.
High swimming costs at low speeds are associated with large induced drag,
while high costs at high speeds reflect energy costs for translocation. In
contrast with other negatively buoyant swimmers, plaice avoid swimming at low
speeds (Fig. 1). As a result,
the rising part of the power curve at h
10 mm at low speeds is
avoided (Fig. 5)
(Duthie, 1982
;
Bartol et al., 2001b
).
When the U-shaped speed/power curve is shallow, the lack of variation in
kinematics with speed is not surprising. In addition to the fin-beat
frequencies of plaice swimming at h0 mm, those of several rays, a
benthic group swimming at the bottom
(Rosenberger, 2001
), and brief
squid (Bartol et al., 2001b
)
are independent of swimming speed or even decrease with increasing speed
(Bartol et al., 2001b
). Thus,
swimming patterns and power production are similar among negatively buoyant
swimmers and these, in turn, are similar to those for flying birds, bats and
insects (Bartol et al.,
2001a
,b
).
Swimming power, height and kinematics
Swimming height had no effect on the kinematics of cod, while plaice
swimming was affected. At h10 mm, the tailbeat frequencies of
plaice were independent of speed (Fig.
4A,B). As h increased from 0 to
10 mm, tailbeat
amplitude increased from 0.06L to 0.11L
(Fig. 4B). The net effect of
these changes in swimming patterns was an increase in the rate of working as
h increased (Fig. 5).
When expressed in terms of the gap/span ratio, PX for the
tail tended to increase monotonically with z/B to a maximum at 1.1
(h=50 mm) (Fig. 6A).
This is similar to the pattern seen for interactions with a wall in trout
Oncorhynchus mykiss (Webb,
1993
), A slight decrease in PX is suggested at
larger values of z/B but, given the normal variation in the input
data, little importance can be attached to this decrease.
|
The relationships between z/B and power are consistent with
observations in other systems that small changes in z/B when this
ratio is small have larger effects on power output. This may explain the lower
amplitude of the tailbeat of plaice swimming at the bottom compared with
swimming at h10 mm. For plaice swimming at the bottom,
z/B averaged 0.23 (Table
2). If the tail amplitude were the same on the bottom as at
h
10 mm, z/B would increase to 0.3. Plaice would then
require approximately twice as much power to swim
(Fig. 6A).
For Bmax, Px increased as z/B max increased from 0.04 (h=0 mm) to 0.1 (h=10 mm) but then decreased at larger values of z/B (Fig. 6B). The decrease in Px at only the smallest values of z/B may occur because much of the upstream wake is absorbed at the leading edge of re-entrant downstream fins, with insufficient time to develop and interact with the bottom.
Nevertheless, the relationship between power and z/Bmax is such that there would be an advantage to decreasing amplitude at maximum span, as for the tail. Mean amplitudes were lower at Bmax for plaice at the bottom (Fig. 6B), but the difference is not significant. Other unknown factors may prevent substantial modulation of amplitude over the whole body length.
There is also an interaction between h and swimming speed, as
found for trout interacting with walls
(Webb, 1993). For example, at
5 cm s-1, P for plaice swimming with h=10 mm
would have been 7.4 times that at h=0 mm. In contrast, at 45 cm
s-1, P was only three times larger at h=10 mm
than at h=0 mm. Thus, the benefits of ground effects diminish as fish
swim faster. This results from smaller downwash angles as speed increases
(Reid, 1932
;
Lighthill, 1979
).
The interactions between h and u on P may explain the modulation of tailbeat frequency in plaice swimming at the bottom compared with fish swimming at greater heights. Presumably, because of the greater importance of the ground effect at low speeds, plaice swimming at the bottom were able to produce sufficient thrust and lift with lower tailbeat frequencies. However, as speed increases, the ground effect diminishes and resistance increases, requiring proportionately higher tailbeat frequencies.
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Acknowledgments |
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References |
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