First published online September 19, 2008
Journal of Experimental Biology 211, 3147-3159 (2008)
Published by The Company of Biologists 2008
doi: 10.1242/jeb.020263
Pitching stabilization via caudal fin-wave propagation in a forward-sinking parrot cichlid (Cichlasoma citrinellum x Cichlasoma synspilum)
S. C. Ting1 and
J. T. Yang2,*
1 Department of Power Mechanical Engineering, National Tsing Hua University,
Hsinchu, Taiwan
2 Department of Mechanical Engineering, National Taiwan University, Taipei,
Taiwan
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Fig. 1. A forward-sinking parrot cichlid executing a caudal fin-wave propagation
(CFP). (A) Lateral view of the fish with a tilted-down swimming posture: head
down and tail up. A wave of bending passes through the surface of the caudal
fin. The dashed blue line indicates the lateral midline defined as a line
connecting the midpoint of the peduncle base and the fish mouth.
 b is the body angle. CM, the center of mass of the fish
body, is indicated by the black and white checked circle. The yellow curved
lines represent the leading edge of the pectoral fins in A and B. (B) Dorsal
view of the fish. The pectoral fins are simultaneously maneuvering. (C) An
example of a time series of traces of the trailing edge of the caudal fin of a
parrot cichlid executing forward sinking via a caudal fin-wave
propagation (observed from behind the fish and a laboratory-bound reference
frame). These traces illustrate kinematical features of the CFP motion.
T1–T12 denote the time steps
associated with each traces. The black and red filled circles represent the
dorsal and ventral tips, respectively, of the trailing edge of the caudal
fin.
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Fig. 2. Experimental apparatus for stereoscopic digital particle-image velocimetry
(SDPIV) and recording images of the fish motion. This sketch shows the setup
for filming the `parasagittal' flow fields. The parrot cichlid swam freely in
a transparent tank filled with still fresh water. The motion camera was placed
below the tank. A mirror was placed on a side wall of the tank to enhance the
intensity of backward scattered light received by the SDPIV camera. The
viewing angle between the optical axis of each camera and the object plane
norm was 30°.
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Fig. 3. Sketches showing the measurement of the center of mass. (A,B) An
unconscious fish was carefully wrapped in nylon string and then suspended for
photography; the procedure was repeated several times with the string in
different positions each time. (C) The center of mass (CM; indicated by a
black-and-white checked circle) was located by determining the intersection of
any two extensions of the upright nylon strings from photographs.
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Fig. 4. Measurement of the center of buoyancy of a parrot cichlid. (A) To find the
desired straight line on which the center of buoyancy was located, a fish in
an unconscious state was dropped into a simple test section. The test section
(a rectangular, transparent water container) was narrow (width  9 cm),
only slightly wider than the body of the parrot cichlid, so as to prevent the
sinking fish from rolling and yawing and only allowing it to pitch. The
sinking fish was filmed. (B) The straight line sought was simply determined on
drawing a vertical line passing through the center of mass of a non-rotating
fish body. This straight line (red) approximately connected the center of mass
(CM) and the base of pelvic fin. CB, the center of buoyancy of the fish body,
indicated by the blue filled circle.
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Fig. 5. Flow velocity fields of a selected swimming sequence measured on a
transverse plane. The schematic drawings (not to scale) at the top of the
figure illustrate lateral and dorsal views of a fish swimming (nearly
steadily) across the light sheet during forward sinking. For the fish, the
sinking angle was approximately 21°; the body angle was approximately
19°. The average swimming velocity of the fish was approximately 0.05 m
s–1; the beat frequency of the caudal fin was 1.3 Hz. The
angle between the swimming direction and the y–z plane was
approximately 28°. (A–D) The color contour represents the
magnitude of z-direction velocity W, i.e. the out-of-plane velocity;
the in-plane velocities are represented by black vectors. The bold white
curves indicate the projection of the trailing edge of the caudal fin on the
light-sheet plane. (A) The dorsal part of the caudal fin was beating toward
the left side, and the ventral part toward the right side (at approximately
29% of a tail beat cycle that was initiated when the dorsal part of the caudal
fin was at the last right excursion). (B) Both the dorsal and ventral parts of
the caudal fin were decelerating and approaching their lateral beat excursions
(at approximately 50% of the tail beat cycle). At approximately t=0.2
s, both the dorsal and ventral parts of the caudal fin attained their lateral
beat excursions and began to beat toward the opposite side. (C) The
accelerating dorsal and ventral parts of the caudal fin were beating toward
the right and left sides respectively (at approximately 60% of the tail beat
cycle). (D) Both the dorsal and ventral parts of the caudal fin were still
accelerating (at approximately 65% of the tail beat cycle). The bold white
arrows indicate the dorsal and ventral CFP jets that were generated by the
caudal fin executing a caudal fin-wave propagation (CFP). White numbers
(1–4) in A and C indicate vortices adjacent to CFP
jets.
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Fig. 7. Flow velocity fields and vorticity contours of the near-fin wake measured
on a parasagittal (x–y) plane of the light sheet
approximately parallel to, and overlapping, the middle plane of the fish body.
The schematic drawings (not to scale) at the top of the figure illustrate the
lateral and dorsal views of the swimming fish during forward sinking. For the
fish, the sinking angle was approximately 35°; the body angle was
approximately 25°. The average swimming velocity of the fish was
approximately 0.053 m s–1; the frequency of tail beating was
1.3 Hz. The interval between A and B was 0.376 s. (A–D) Black vectors
represent the in-plane velocity; gray areas indicate zones of the light sheet
that were shaded by the maneuvering caudal fin and were unobservable with the
SDPIV cameras. (A,B) The color contour represents the magnitude of the
z-direction velocity W. (C,D) Vorticity contours
corresponding to velocity fields in A and B, respectively. The bold white
curves indicate the projection of the trailing edge of the caudal fin on the
plane of the light sheet. The bold black arrows indicate the dorsal and
ventral caudal fin-wave propagation (CFP) jets generated by the caudal fin
executing a CFP. White P1, P2 and
P3 denote vortices adjacent to the CFP jets; the white
curved arrows indicate the directions of rotation of vortices
P1, P2 and P3.
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Fig. 8. Wake of the pectoral fin measured on a parasagittal
(x–y) plane of the light sheet approximately parallel
with the fish body and intersecting the pectoral fin. The schematic drawing
(not to scale) at the top of the figure shows a lateral view of a swimming
fish during forward sinking. The average swimming velocity of the fish was
approximately 0.066 m s–1; the sinking angle was
approximately 27°; the body angle was approximately 20°. (A–C)
Instantaneous velocity fields of the wake for the down-stroke, stroke reversal
and up-stroke, respectively. The time was set to t=0 s for A; (B)
t=0.064 s; (C) t=0.224 s. The black vectors represent the
in-plane velocity in A–D. The color contour represents the magnitude of
the z-direction velocity W in A–C. (D–F)
Vorticity contours corresponding to the velocity fields in A–C,
respectively. The bold black arrows indicate the fluid jets generated by the
pectoral fin. White K1, K2 and
K3 denote vortices adjacent to the down-stroke and
up-stroke jets. The white and curved arrows indicate the directions of
rotation of vortices K1, K2 and
K3. A three-dimensional down-stroke jet (A) and an
up-stroke jet (C) were observed.
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Fig. 9. Schematic drawings (not to scale) that illustrate the fluid jets generated
by a caudal fin-wave propagation (CFP) and the pectoral fins in a
forward-sinking parrot cichlid executing a CFP. (A) Lateral view, with the
CFP, down-stroke and up-stroke jets indicated by green, red and blue arrows,
respectively. CM, center of mass of the fish body, indicated by a white and
black checked circle; CB, center of buoyancy of the fish body, indicated by a
blue filled circle. The straight line connecting the CM and the CB is shown
(dashed line). (B) CFP, down-stroke and up-stroke jets observed from behind
the fish. The colored numbers adjacent to the jets denote the temporal order
of formation of the jets in A and B; only the expelled CFP jets are
displayed.
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Fig. 10. Schematic drawing (not to scale) that illustrates the pitching-moment
balance in a forward-sinking parrot cichlid adopting a tilted-down swimming
posture. The caudal fin wave of the parrot cichlid propagates dorsally. The
purple curved thick arrows represent the induced pitching moment.
MB is the head-down pitching moment induced by the buoyant
force (FB). MPF is the head-down
pitching moment induced by the down-stroke force (FPFD) of
the pectoral fin; MCFP is the head-up pitching moment
induced by the caudal fin-wave propagation force (FCFP). The
behavior of a CFP functionally facilitates the pitching stabilization.
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Fig. 11. Sequential two-dimensional schematic drawings (not to scale) summarizing
the formation of a near-fin wake and the evolution of caudal fin-wave
propagation (CFP) jets observable in a forward-sinking fish executing a CFP.
These drawings pertain to observations made from behind the fish. (A–D)
Flow patterns observed at approximately the 1/3, 1/2, 4/5 and end phases,
respectively, of a CFP beat cycle. The black bold lines represent the trailing
edge of the caudal fin; the black filled circle represents the dorsal tip. The
colored arrows indicate CFP jets (designated Jet 1, Jet 2 and Jet 3) generated
by the caudal fin. The dashed circles with arrows represent vortices (denoted
a–g) adjacent to the CFP jet. The temporal order of formation is Jet 1,
Jet 2 and then Jet 3.
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Fig. 12. Three-dimensional sketches that illustrate the proposed (A) near-fin and
(B) far-fin wake of the caudal fin-wave propagation (CFP). The curved black
arrows indicate the direction of vortex rotation. (B) The two-dimensional
sketch at the upper right illustrates the vortex filaments of the far-fin wake
observed on a parasagittal plane. Dashed lines and arrows indicate the vortex
filaments and their directions. The feature of the slightly divergent
configuration of a CFP jet is not illustrated here.
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© The Company of Biologists Ltd 2008
2-value and vorticity for the flow field
shown in Fig. 5C. (A)