## SUMMARY

The kinematics of plaice (*Pleuronectes platessa, L*=22.1 cm) and
cod (*Gadus morhua, L*=25.0 cm, where *L* is total fish length)
swimming at various speeds at the bottom and lifted to heights, *h*, of
10, 50 and 100 mm by a thin-wire grid were measured. For cod, tailbeat
frequency, amplitude, body and fin span and propulsive wavelength were
unaffected by *h* and varied with speed as described for fusiform
pelagic species. In contrast, the kinematics of plaice was affected by
*h*. Body and fin spans and propulsive wavelength were independent of
swimming speed and *h*. Tailbeat amplitude was independent of swimming
speed, but averaged 1.5 cm at *h*=0 and 2.5 cm at *h*≥10 mm.
Plaice tailbeat frequency increased with swimming speed for fish at the bottom
but was independent of swimming speed at *h*=10, 50 and 100 mm,
averaging 4.6, 6.0 and 5.8 Hz respectively. Total mechanical power,
*P*, produced by propulsive movements calculated from the bulk-momentum
form of elongated slender-body theory was similar for cod and plaice swimming
at the bottom but, at *h*≥10 mm, *P* for plaice was larger
than that for cod. Plaice support their weight in water by swimming at a small
tilt angle. The small changes in swimming kinematics with swimming speed are
attributed to decreasing induced power costs to support the weight as speed
increases. The contribution of the tail to power output increased
monotonically with the tail gap/span ratio, *z/B*, for
*z/B*=0.23 (*h*=0 mm) to *z/B*=1.1 (*h*=50 mm).
The smaller tailbeat amplitude of the tail decreased both *z/B* and the
power output for plaice swimming at the bottom. For the maximum body and fin
span of plaice, the contribution to power output increased for local
*z/B* values of 0.044 (*h*-0 mm) to 0.1 (*h*=10 mm) and
declined somewhat at larger values of *z/B*. The smaller effect of the
bottom on power output of the largespan anterior body sections may result from
the resorption of much of the upstream wake at the re-entrant downstream
tail.

## Introduction

Most fishes live in cluttered habitats characterized by structures such as surfaces, struts (e.g. large woody debris) and protuberances (e.g. boulders). These habitats are typically productive and support a rich fauna of benthic fishes (Moyle and Cech, 1996). Many benthic fishes are flattened in the plane of the substratum and negatively buoyant, especially when there are currents for which these features facilitate station-holding (Arnold and Weihs, 1978). The most flattened groups are found among the pleuronectiform flatfishes, batoid rays and more ray-like selachians. These fishes also have large body spans, probably to help maintain body volume in spite of body flattening.

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.

## Materials and methods

### Fish

Fish, plaice (*Pleuronectes platessa*) and cod (*Gadus
morhua*), were caught near Lowestoft (England) using beam trawls. They
were held in 12001 tanks, continuously aerated and flushed with filtered sea
water at 15°C for 4-6 weeks before the start of experiments. Fish were fed
on chopped lugworm, mackerel and herring.

### 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 m×0.3 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:
1
where *z*_{1,bottom} is the distance above the bottom (ground)
at one extreme of the tailbeat and *z*_{2,bottom} is the
distance above the bottom at the other extreme, *z*_{1,boat} is
the distance below the boat at one extreme of the tailbeat and
*z*_{2,boat} is the distance below the boat at the other
extreme.

In addition, the ground effect is small at *z/B*≈2 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, *z*_{1,bottom}=*h*. At the other extreme of the
tailbeat amplitude, *z*_{2,bottom}=*h*+*H*, where
*H* is the amplitude of a beat. For the special case of *h*=0,
*z*_{1,bottom} is zero and mean
*z*_{bottom}=*H*^{0.5}. The total depth
available was limited to 29 cm, so that
*z*_{1,boat}=29-*h*, and
*z*_{2,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} (Δ*u*) every 10 min (Δ*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 (*u*_{crit}) was calculated as described by Brett
(1964): 10-min
*u*_{crit}=*u*_{p}+Δ*ut*/Δ*t*,
where *u*_{p} 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 α≤0.05.
Descriptive statistics are reported as means ± 2 S.E.M. (see
Sokal, 1995).

## Results

### Limits of swimming speeds

Cod and plaice held station on the bottom without swimming at low current
speeds, as described previously (Arnold,
1969; Arnold and Weihs,
1978; Webb, 1989).
Cod began swimming at an average speed of 9 cm s^{-1}
(Fig. 1). These swimming speeds
were independent of *h* (ANOVA, *P*>0.9). Plaice began
swimming at current speeds of 15-25 cm s^{-1}. Swimming speeds on the
grid at different values of *h* were not significantly different from
each other (*P*>0.8). As found elsewhere
(Webb, 1989), swimming speed
was higher for plaice at the bottom compared with the average for the grids
(*t*-test, *P*<0.01), and plaice swimming speeds were
significantly larger than those of cod (ANOVA, *P*<0.05).

The 10-min *u*_{crit} 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 *u*_{crit} of
plaice was unaffected by height for *h*≥10 mm, averaging 46 cm
s^{-1} (ANOVA, *P*<0.08). The mean 10-min
*u*_{crit} 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, λ, was independent of both speed and swimming height
(ANOVA, *P*>0.9). Wavelengths averaged 16.4±0.2 cm
(*N*=259) (0.74*L*, where *L* is fish total length) for
plaice and 23.3±5.7 cm (*N*=158) (0.93*L*) for cod.
Plaice swimming was therefore more anguilliform than that of cod.

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 0.16*L* at the trailing edge to a minimum
of 0.03*L* at a distance of approximately 0.3*L* from the nose.
Specific amplitude then increased over the head to 0.04*L* 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
0.19*L*, respectively) over the same range of speeds so that
*H*=(2.5±0.2)+(0.039±0.007)*u*,
*r*^{2}=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).

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
(0.07*L*) for plaice swimming at the bottom, compared with amplitudes
of 2.4-2.6 cm (0.11-0.12*L*) at *h*≥10 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 0.7*L* 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 0.07*L* for plaice swimming at the bottom and
0.11*L* 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
0.28*L* for cod occurred at 0.5*L* 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 0.2*L* at 0.75*L*
along the body, which in turn exceeded the maximum span at the caudal fin of
0.16*L*. 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 0.55*L* occurred at
0.45*L* from the nose (Fig.
3D). Span initially decreased continuously from this maximum over
the posterior of the body, before increasing to 0.25*L* at the caudal
fin. The trailing edge of the caudal fin was convex so that the maximum tail
span occurred at approximately 0.1*L* 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) (0.16*L*) for cod, representing 89 %
of the potential depth. For plaice, swimming tail span averaged 5.2±0.1
cm (*N*=158) (0.24*L*), 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
(*z*_{tail}/*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/B*_{max}
was smaller, varying from 0.04 to 1 over the same range of *h*.

## Discussion

The goal of these experiments was to determine the consequences of swimming near the ground by benthic fishes, especially for plaice whose body shape and posture could provide substantial benefits from ground effects. In general, the swimming motions of cod were typical of other species swimming in the water column (Webb, 1975; Videler, 1993; Webber et al., 2001). Tailbeat frequency and amplitude varied with speed, especially the former. The span of the trailing edge and propulsive wavelength were constant. These were not affected by swimming height. Cod therefore derived no benefit from the ground effect.

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,
*P*_{X}, is:
2
where:
3
4
5
and ρ_{water} is the density of sea water, *M* is added
mass per unit length of an element, *W* is the mean lateral speed
assuming sinusoidal motion, *w* is the velocity given to the water,
*B*_{X} is the local span, *F*_{X} is the local
tailbeat frequency, *H*_{X} is the local amplitude and
*c*, the backward speed of the propulsive wave, is equal to
*F*λ.

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
*P*_{X} 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 *B*_{max} at
0.45*L* measured from the nose until body and fin span equaled the tail
span at 0.7*L* (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.

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 *h*≥0 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 *h*≥10 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 0.06*L* to 0.11*L*
(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, *P*_{X} 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 *P*_{X} 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 *h*≥10 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 *B*_{max}, *P*_{x} 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
*P*_{x} 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/B*_{max}
is such that there would be an advantage to decreasing amplitude at maximum
span, as for the tail. Mean amplitudes were lower at *B*_{max}
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.

- Symbols
- 10-min
*u*_{crit} - 10 min critical swimming speed
- B
- span, the depth of the body and fins
*B*_{max}- maximum span
*B*_{x}- local span
- c
- backward speed of the propulsive wave
- F
- tailbeat frequency
*F*_{x}- local tailbeat frequency (equal to
*F*) - H
- amplitude of a tailbeat
- h
- height of the thin wire grid above the bottom, swimming height
*H*_{x}- local amplitude
- L
- total length of a fish
- M
- added mass per unit length of an element
- P
- mean rate of working
*P*_{x}- mean rate of working for an element at
*x* - u
- swimming speed
*u*_{p}- penultimate swimming speed before failure in the calculation of
*u*_{crit} - W
- mean lateral speed assuming sinusoidal motion
- w
- velocity given to the water
- x
- position along the body centerline
- z
- gap, the space between a solid surface and the thrust-producing body and fins
- z/B
- gap/span ratio
*z/B*_{max}- gap/span ratio at the maximum span
*z*1,boat- distance below the boat at one extreme of the tailbeat
*z*1,bottom- distance above the bottom (ground) at one extreme of the tailbeat
*z*2,boat- distance below the boat at the other extreme
*z*2,bottom- distance above the bottom at the other extreme
- ztail/B
- gap/span ratio for the tail
- Δt
- time between current speed increments
- Δu
- current speed increment
- λ
- length of propulsive wave
- ρwater
- density of sea water

## ACKNOWLEDGEMENTS

Support was provided by NSF grants IBN 9507197 and IBN 9973942. I thank the staff at the Lowestoft CEFAS laboratory, especially Dr G. P. Arnold and J. Metcalfe for the providing facilities and assistance.

- © The Company of Biologists Limited 2002