ABSTRACT
Pacific Sand dabs exibit postural change when introduced to flow,
The rheotaxis and the underlying hydrodynamics are not well studied for
flatfish. No known values for lift or drag exist. In this study force
transducers were used to measure drag and lift on the sand dab, and
corresponding drag and lift coefficients were calculated. The lift is
remarkably variant with altered posture anddrag is virtually unchanged.
It is this four fold lift reduction for head to tail flow that enables
the sand dabs to stay in place in currents up to 402 to 50% faster,
The sand dab is equally efficient with flows in the opposite direction;
this is essential to accommodate the bidirectional surge. A mechanism
for lift reduction, or more importantly for increased slipping velocity,
is proposed.
INTRODUCTION
The Pacific Sand dab, Citharichthys sordidus is a bottom dweller
in ocean depths from 30 feet to 1600 feet. The flatfish is well designed
for sea floor inhabitation and would prefer to stay camouflaged on the
bottom. At depths of 30 feet with wave height of 10 feet and a period of
10 seconds, wave surge can reach surprising velocities of V = 150 cm s-l.
Surge of this magnitude means sand dabs are exposed to significant flows
with dislodging potential. Sand dabs exibit a rheotaxis or reaction
to water flows in an attempt to withstand larger flow speeds. Arnold,
C
1969 observed similar behavior in plaice and Arnold and Weihs, 1978
studied the hydrodynamic factors underlying the rheotaxis in plaice.
Empirically measured values of lift and drag force, and in particular
the lift and drag coefficients, remain unknown for flatfish. The
combination of streamline and aerfoil shapes make sand dabs a unique
hydrodynamic study, and proves to help explain the function of the
rheotaxis.
MATERIALS AND METHODS
Flow Tank
Experimentation was done in a flow tank similar to that described
by Vogel and LaBarbera, 1978 (figure 1). A constant flux of sea water
kept the temperature in a range of 13 to 15 C. Tlow speeds reached 106
cms. These mainstream speeds were measured by timing fluorescein dye
over a one meter distance.
Live Fish
Sand dabs were caught with hook and line and kept in a sandy bottom
holding tank, receiving a constant supply of sea water. The temperature
was 10 to 12°C. The sand dabs were fed freshly killed fish three times
weekly. Fish length ranged from 16.5 to 21.0 cm. The fish densities
were calculated from the equation (where mis the mass in air,
mthe submerged mass and o is the density of sea water. The average
fish density was 9-1.055 x 10 kg m-3.
Model Fish
Models were made of silicone rubber imbedded with wire for rigidity,
A sand dab was killed in a water bath containing a high concentration
of MS 222, resulting in minimal physical alterations of the fish. The
fins were carefully spread and pinned down, and the fish was then frozen.
Parafin wax was poured over the prepared fish forming the mould. A
layer of silicone rubber was applied, followed by five wires and the
final layer of rubber. Aluminum foil fins backed by fine wire were
used to replicate dorsal and anal fins.
The model was 17.1 cm. in length and slightly more dense than the
live fish (P = 1.062 10° kg m2). The blotted mass was m = 48.7g
and the submerged mass m,- 1.8 g. Maximum width measured from anal to
dorsal fin was w - 8.3 cm.
Transducers
Twotransducers were used to measure forces on the model sand dab,
Both the drag and lift transducers were made of acrylic plastic and
designed to rest in the top portion of the flow tank (figures 2 and 3).
The model was attached to a double-cantilever beam. Any force applied
to the model resulted in a proportional displacement of the beam. These
displacements were sensed by a linerly variable differential transformer
and recorded on a voltmeter. After weight calibration the drag trans¬
ducer had a linear regression line with the equation F, = 1.180 V - .002,
r 7 .999 where Fy is the drag force and V is the voltage reading. The
lift transducer yielded the equation Fj = 2,25 V + .002, also with r».999;
Fj is the lift force. Since measured lift forces approached zero the
adjusted equation Fj = 2.32 V was used for voltage readings less than
or equal to.008 V.
The model was mounted to the moveable beam with a screw to allow
easy removal and posture adjustments. When attached to the transducers
and lowered into the tank, the model was inverted with its ocular side
down.
Use of the transducers required velocity adjustments due to the
constriction of flow by the transducer. The speed adjustment for the
drag transducer was U = 1.27 U, and U = 1.25 U, for the lift transducer.
Uo is the original mainstream velocity and U is the adjusted velocity.
The estimated error for voltage readings is se= .002 for both trans¬
ducers.
Manometer
Manometry was used to estimate the lift force on the model. An
inverted, sloped manometer (Vogel, 1981) was filled with corn oil with
a measured density of p =.912 10° kg m23. One pressure probe was
stationary beneath the fish on the lateral line. The second probe
measured the constant mainstream water pressure. Values were recorded
for flat and fins up postures. For more information on manometry,
see Vogel, Life in Moving Fluids.
Inclined Plane
Static friction coefficients, M., were measured with an inclined
plane apparatus (figure 4). Values were calculated from an average
angle of slippage, 6, using the equation - tan 0. (This is
g. - mg sin e and Fy = mg cos 0. Sub¬
derived from Fg - Fy. E
stitution results in P= tan 0.) The plane had an acrylic plastic
surface to mimic the flow tank floor and all measurements were made
while the apparatus was submerged in sea water.
Experimental Procedure
The rheotactic behavior of live sand dabs was observed in the flow
tank, with careful note of current velocities. Fish were centered in
the tank and oriented in the desired direction. Speeds were increased
in 5 cm s4 increments with a minimum of 5 minutes between changes.
Similar observations were recorded for the model sand dab.
Transducer measurements varied with model shape and distance from
transducer. Precautions were taken to consistently mimic the rheotactic
response with the model. It was found necessary to remove all air
bubbles trapped between the model and the transducer apparatus.
The drag transducer was tested with a 1/2 inch in diameter cylinder.
The drag coefficient was C = 0.58. Recorded values for similar shaped
cylinders are C = 0.48 to Cq = 0.75 (Hoerner, 1965).
BEHAVIOR
Sand dab Rheotaxis
Sand dabs undergo a remarkable series of behaviors when introduced
to flow (figure 5). When no flow exists sand dabs typically settle on
the tank bottom, head raised up to 2 cm off the substrate. As head to
tail flow begins the head is lowered. With increasing flow most fish
commence burying movements. This behavior consists of rapid body un¬
dulations coordinated with anal and dorsal fin beating. In addition
to being used as a settling device while on sand, it appears to help
extrude water from beneath the fish. This results in increased surface
area in contact with the substrate. The burying movements seem to ac¬
complish results similar to the "posterior fin-beating response" described
by Arnold, 1969.
As flow increases, dorsal and anal fins are raised into a fins up
posture (figure 6). This entails a characteristic raising of the poster¬
ior portion of the anal and dorsal fins. This is coupled with a notice¬
able body arch directly above the posterior region and a slight upward
cambering along the length of the body. Also the fins up posture
creates a water channel along the length of the dorsal side. The flow
originates from a small adjustment of an anterior portion of the
dorsal fin. A natural channel exists on the ventral side. This channel
results from the inability of the anal fins to contact the substrate.
This posture is the most intruiging behavior as these changes cause
significant flow redirection enabling the fish to stay stationary longer.
Flows moving from tail to head elicit a different series of reactions
from the sand dabs. No burying movements are observed and the fins up
posture is never noted. Some fish also slip slightly sooner when flow
moves from tail to head. Neither arching nor cambering is observed
as the flat posture appears most beneficial for remaining in place.
THEORY
Hydrodynamics
Rheotaxis suggests that as flows increase fish alter their posture
to postpone slippage. Sand dabs orient randomly when placed in the
flow tank and with the initiation of flow, do not appear to prefer one
flow direction to the other. Arnold and Weihs, 1978 theorize that the
head to tail flow is hydrodynamically advantageous based on the decreased
drag force on the streamlined body. But lift force is probably greatest
in this orientation, and the resultant slipping speed is an intricate
balance between these two forces.
The current initiates a drag force on the fish in the direction
of flow. This drag is the sum of pressure drag and skin friction drag.
The characteristicly gradually tapering tail of the streamlined sand
dab delays the separation point and results in relatively low pressure
drag (Blake, 1983). Blake, 1983 suggests that for a streamlined object
most of the drag is a result of skin friction drag.
Total drag force can be calculated from the equation
Fa - 1/2 Ca.Ap U2
where F, is the total drag froce, C the drag coefficient,? the density
of sea water, Ag the plan area and U is the flow speed. When the
total drag force exceeds the frictional force the fish can no longer
remain in place and slips downstream. The slippiay threshold can be
calculated from the equation
Fa -MsW,
(2)
where Lis the static friction coefficient and W is the effective
weight of the fish.
Since the streamline shape of the sand dab is also an aerfoil, a
lift force is created. This force directly opposes the submerged weight
(figure 7) such that
W - Wo - Fy.
(3)
where W, is the submerged weight and Fj is the lift force. The lift
force is defined as
Fi - 1/2 C(.Ap U2,
(4)
where Cj is the lift coefficient.
Combining equations 1-4 one can solve for the slipping velocities,
2 Wo
1/2
Ug -
(5)
A (C1 19
1. Cg and uare all unknown for live sand dabs. It is possible to
calculate C, and C from forces measured on models. Mg values are also
obtainable. U, can then be calculated and compared to the observed
values. This serves as a check for the C and C, calculations.
Since lift and drag forces increase by the square of the flow
velocity, a small flow increase results in a large combination of forces
acting on the fish. If the sand dab wishes to remain stationary, any
posture change that can reduce either lift or drag force is quite ad¬
vantageous.
RESULTS
Lift and Drag
The fins up posture results in a significant reduction in lift
force (figure 8). The decline in lift is roughly 4 fold at all
velocities. The drag force is not significantly changed by altered
posture. The lift force is on the average, two times that of the drag
force in the flat posture at all flow speeds. However with the fins
up, the calculated lift is one half that of the drag force.
Lift and Drag Coefficients
The calculated drag and lift coefficients both vary over the
Reynolds number range of 10’ to 10°. No substantial change in C
resulted from a change in posture (figure 9). C on the other hand,
dropped drammatically during the fins up posture to nearly 25% of
the flat posture value (figure 10).
Flow direction had no effect of C at a speed of U - 30 cm s i
(approximate slipping speed) (figure 11). C however, shows substantial
change with flow direction.
Manometry
The pressure difference between the flat posture and the fins
up posture was measured to be AP = 2.59 N m2. For a plan area
A = 7.5 10 ° m2 the lift reduction from the fins up posture was
thus predicted to be F = .019 N.
Static Friction Coefficient
Sand dabs freshly anesthitized in MS 222 had a calculated static
friction coefficient of M-.30. This value is similar to that of
freshly killed plaice where M, -.2 to .4 (Arnold and Weihs, 1978).
A, for the model was much higher due to the nature of the silicone
rubber and perhaps, the absence of mucus. Values averaged M,=.84
for the flat posture and M,- .75 for the fins up posture.
DISCUSSION
Lift and Drag
Simple observation suggests that sand dab rheotaxis alters the
interaction of drag and lift: A model in the fins up posture slips at
35 cm s+ while the same model in the flat posture slips at 30 cm s 1.
An anesthetized fish slips around 20 cm s1,
Hydrodynamic analysis supports this conjecture. The lift reduction
produced by the fins up posture increases the effective weight, W, and
thereby frictional force. Since the drag force is unchanged the fish
effectively postpones slippage (figure 12). From equation (5), the
model in the flat posture with head to tail flow, U. - 20.7 cm s'i
(Cg and C, values at Reynolds number Re = 6.5 «10“ , the approximate
slipping velocity of U = 30 cm s1). For the same flow direction in
the fins up posture Ug = 26.8 cm s1.
Is the model a good simulation of live sand dabs? Plotting
frictional force and drag force as a function of flow speed (from
equation (5) with Mg-.30 for the live sand dab) U - 16.6 cm si
(figure 13). This value is one-half the value observed. The low
prediction is explained in three ways. (1) g was calculated for
anesthitized fish and found to be Us -.30. It is likely that
conscious fish can physically increase  through fin use and general
body conformation. As already mentioned, burying movements increase
surface area in contact with the substrate, and perhaps increases the
value of A.. This directly increases frictional force and delays
movement. (2) Although the model is a good replica of sand dab shape
it does lack mucus. Daniel, 1981 reported that skin friction can be
reduced up to 502 in turbulent or pulsed laminar flows. Since skin
friction is an important component of total drag in streamline objects,
mucus is likely to decrease total drag. A decreased drag means an
increased U.. Together, these two changes could shift the slipping
speed into the observed range. (3) The observed slipping velocity
may also be at fault. The flow tank creates a substantial boundary
layer. The measured mainstream flow was the value observed at the
slipping speed. The actual flow speed acting on the fish is less than
mainstream flow due to this velocity gradient. Hence, the observed
U. is greater than the calculated value from equation (5).
C and
Since C, and C, have never been quantitatively determined for sand
dabs, only rough comparisons can be made to shapes of known coefficients
(figure 14). Drag of an asymmetric semi-ellipsoid body with its blunt
end facing the flow depends on its fineness ratio or ratio of length
to thickness. For minimum drag the optimum value is between 10 to 15
(Blake, 1983). For sand dabs the ratio is between 12 and 13. The
corresponding minimum drag coefficient is C, -.03 for the semi-ellipsoid
body. Drag coefficients for the model sand dab range from C = ,O1
to C -.045.
Arnold and Weihs, 1978 estimated Cj and C, for plaice (Pleuronectes
platessa L. ) and concluded that C was 10 to 20 times Cq. But in
doing so it is necessary to assume that  is constant for Re » 10',
This assumption is invalid for sand dabs as both Cq and C vary over a
small Reynolds number range of Re = 104 to Re = 10°. The sum is also
not constant. The actual ratio of lift to drag in sand dabs is 1/10 th
that theorized for plaice.
A partial explanation for the difference stems from basic geometry.
The plaice has a larger aspect ratio, ratio of width to length, than
does the sand dab. However the former results in increased lift (Blake,
1983). This accounts for a fraction of the ten fold difference. The
remaining difference is most probably due to the assumption of a constant
- value. Empirical evidence (figures 9 and 10) shows this assump¬

tion to be invalid in sand dabs and perhaps flat fish in general.
Lift Reduction Mechanism
It is well substantiated that rheotaxis reduces lift force, and
therefore increases the slipping velocity. The mechanism behind lift
reduction is hypothesized to be increased flow speed beneath the sand
dab. The flow originates primarily from water channels along the dorsal
and anal fins. The raised fins serve as the outlet channel where water
exits from beneath the body. Fluorescein dyes used to study currents
support this theory.
A manometer confirms the increased flow during the fins up posture
The measured drop in force of F =.019 N during the fins up posture is
evidence of a decrease in pressure beneath the fish. From Bernoulli's
principle it follows that flow velocity must increase. So the rheotaxis
is merely a hehavioral reaction to reduce lift by increasing flow beneath
the body.
The manometer result of F =.019 N is less than the transducer
measurement of F - .025 N for lift reduction from the fins up posture.
The difference is explained by rough manometer procedure. Only one
point beneath the fish was measured, that being under the arched section
on the lateral line. This point is posterior to the center of lift and
should theoretically yield a smaller value.
The sand dab has developed a clever hehavior to increase slip
speed for head to tail flows. But wave surge is bidirectional. To
remain in place on the bottom with flow from tail to head, the sand dab
doesn't raise his fins. C =.014 for the flat position. This value
is not significantly different from the Cq -.016 calculated for the
fins up posture in head to tail flow.. Sand dabs theoretically could
combat the bidirectionality of wave surge then, by subtle changes in
posture. For head to tail flow the fins up posture is best and for
the reverse flow the flat posture is most advantageous. Since no single
flow direction is hydrodynamically preferred, the sand dabs can avoid
constant reorientation to changing flow directions.
SUMMARY
(1) Sand dabs exibit a behavioral response to flow.
(2) The rheotactic response is characterized by the fins up posture
where posterior anal and dorsal fins are raised, the body arches in
this same region, a water channel is created on the dorsal side, and
there is a slight upward cambering the length of the body.
(3) This posture change reduces lift by a factor of four, while drag
forces are unchanged. The result is an increased slipping velocity.
(4) The slipping velocity prediction for live sand dabs suggests that
either a) M.is larger or highly variable for the live fish. b) the
drag force and coefficients are slightly high. c) the observed slip¬
ping velocities are too high, a result of the velocity gradient of
the flow tank.
(5) Drag and lift coefficients are not constant over a Reynolds number
range of Re = 104 to Re = 105.
(6) For head to tail flow the fins up posture is hydrodynamically favor¬
able. For opposite flow the flat posture is the most effective. The
sand dab feels essentially equal forces in either flow direction.
(7) The proposed mechanism for lift reduction is an increase in flow
beneath the body thereby decreasing the pressure beneath the fish.
ACKNOWLEDGEMENT
I feel fortunate to have studied under a perfect blend of
Man
faculty.
ks to Bill Gilly, Chuck Baxter, Mark Denny, and
Freya Sommer for endless kno
adge and the time to share it. I
am deeply indebted to Mark Denny whose ingenuity and tolerance
reined me through my entire project. And lastly to the class...
what a sense of humor!
REFERENCES
Alexander, M.R. (1983). Animal Mechanics. Blackwell Scientific
Publications, Oxford. PP 183-233.
Arnold, G.P. (1969). The Reactions of the Plaice (Pleuronectes platessa
L.) to Water Currents. Journal of Experimental Biology. 51, 686-697.
Arnold, G.P. (1978). The Hydrodynamics of Rheotaxis in the Plaice
(Pleuronectes platessa L.). Journal of Experimental Biology. 75,
147-169.
Blake, R.W. (1983). Fish Locomotion. Cambridge University Press,
Cambridge.
Daniel, T.L. (1981). Fish Mucus: In Situ Measurements of Polymer Drag
Reduction. Biological Bulletin. 160, 376-382.
Hoerner. (1965). Fluid- Dynamic Drag. Self-published.
Vogel, S. (1981). Life In Moving Fluids. The Physical Biology of Flow.
Willard Grant Press, Boston.
Vogel, S. and LaBarbera, M. (1978) Simple Flow Tanks for Research and
Teaching. Bioscience. 28,638-643.
FIGURE LEGENDS
Figure 1. Flow tank made of PVC pipe and acrylic plastic. The
filters are used to facilitate laminar flow. See Vogel and LaBarbera,
1978.
Figure 2. Drag transducer. The model is attached to a double¬
cantilever beam. Any force acting on the model results in displace¬
ment of the beam, and is recorded by the linearly variable differential
transformer.
Figure 3. Lift transducer.
Figure 4. Inclined plane apparatus used to measure the frictional
coefficient of live and model fish.
Figure 5. Sand dab reactions to flow.
Figure 6. Fins up posture. Characterized by raised fins, arched
body, dorsal side water channels, and an upward cambering of the
body.
Figure 7. Forces acting on the sand dab experiencing flow,
Figure 8. Lift reduction through postural change.
flat posture
———- fins up posture
The drag coefficient is not constant. Postural change
Figure 9.
results in no alteration of the drag coefficient
flat posture
———- fins up posture
Figure 10. The lift coefficient is not constant. Postural change
results in a drammatic change in the lift coefficient.
flat posture
— fins up posture
Figure 11. Drag is unchanged with flow direction and posture. Lift
shows signigicant change with both flow and posture.
Figure 12. Slip speeds (Ug) and lift speeds (U,) for the model sand
dab.
fins up posture
——- flat posture
Figure 13. Predicted slip speeds (Ug) and lift speeds (Uj) for a
live sand dab with effective weight of 1.8 g and u. - ,30.
Figure 14. A comparison of drag coefficients at Re = 102 for plan
area.
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