First published online October 17, 2008
Journal of Experimental Biology 211, 3359-3369 (2008)
Published by The Company of Biologists 2008
doi: 10.1242/jeb.020917
Hydrodynamics of the escape response in bluegill sunfish, Lepomis macrochirus
Eric D. Tytell1,* and
George V. Lauder2
1 Department of Biology, University of Maryland, College Park, MD 20742,
USA
2 Department of Organismic and Evolutionary Biology, Harvard University,
Cambridge, MA 02138, USA
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Fig. 1. (A) Top view of filming and laser configuration, approximately to scale.
Laser light sheets from two lasers (`laser 1' and `laser 2') oriented at 90
deg. to each other were used to avoid shadows. Particle motion was filmed from
below. The ventral camera is not shown but its field of view is indicated by a
square. Both cameras acquired images synchronously at 1000 fps, with
1024x1024 resolution for ventral camera and 1280x512 for lateral
camera. The location of the stimulus is shown with a white circle. A lateral
camera was used to determine the position of the fish in the light sheet. A
slow flow from left to right was used so that the fish would maintain a
consistent orientation. (B,C) Example images from the ventral camera (B) and
lateral camera (C). Note that in the lateral view, C, only a portion of the
fish's upper body can be seen in the bright laser light.
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Fig. 2. Number of trials with the laser light sheet at four different
dorso–ventral positions. Light sheet height was measured at half the
body length of the fish at the end of stage one. Inset shows the light sheet
angles that varied slightly as individual fish were slightly tilted in some of
the sequences. Different colors represent different individuals. A silhouette
of the fish is shown in the background as a guide to the light sheet
positions, so that the width of each bar represents the approximate range of
positions.
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Fig. 3. Distribution of fish mass. (A,B) Fraction of total fish mass in transverse
(A) or horizontal (B) slices. Dotted lines indicate the approximate thickness
of each slice. (C) Estimated mass distribution across the fish body. Color
indicates the mass per lateral area, normalized by the fish's mass m
and the length L.
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Fig. 4. Kinematics from a typical C-start. (A) Silhouettes of the body in its
initial position (black), at the end of stage one (gray) and at the end of
stage two (open). The location of the center of mass (COM) over time is shown
with a red line with dots every five milliseconds. White crosses mark the
initial position and positions of stage one and stage two. (B) Velocity of the
center of mass over time. Divisions between stage one and two are shown with
dotted lines. (C) Angular velocity of the head over time.
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Fig. 5. Images of a typical bluegill sunfish C-start showing the associated
hydrodynamic flows at the mid-body level (yellow velocity vectors). Note that
only every fourth vector is shown for clarity. The stimulus is visible in the
lower left of each panel, and the three dominant jet flows are labeled (see
text for discussion). The strong suction on the inside of the C-bend is
clearly visible in panel B. Note that jet one represents momentum that largely
opposed the fish momentum along the final trajectory. Vectors in the region of
the stimulus in the lower left corner of each panel and over the fish body
have been deleted. The bluegill icon at the bottom indicates the position of
the light sheet (black line) in this sequence and a time-line for this
sequence is shown. Peak flow velocities are nearly 1 ms–1. In
this escape, stage one lasted for 32 ms and stage two for 25 ms, therefore,
the whole escape lasted 57 ms.
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Fig. 6. C-start escape responses showing flows resulting from motion of the dorsal
(A) and anal (B) fins. Bluegill icons at the top of each panel indicate the
position of the light sheet (black line) for each panel. The stimulus
generating the escape was just off the lower left corner of each image. Both
images are from the end of stage one. (A) Jet one and the dorsal fin portion
of jet two are shown. The protruding fin is the anal fin. (B) The anal fin
portion of jet two is shown. Jet one is not visible because the light sheet
for this trial was located just below the caudal fin. In both panels, every
second vector is shown for clarity.
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Fig. 7. Flow and vorticity for a fast start with the light sheet intersecting the
lower body. Vectors show the flow with brighter green colors indicating high
velocity. Red and blue colors indicate counter-clockwise and clockwise
vorticity, respectively. Broken ovals with numbers show the outlines of
identified jets. The fish silhouette is shown in gray. The inset shows the
light sheet position on the body. The time starting from the first visible
movement is shown at the top of each panel, and a time-line for this escape is
shown at the bottom right.
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Fig. 8. Fluid momentum matches the fish momentum parallel to the final trajectory.
Momentum in each jet is shown for stage one (solid bars) and stage two (open
bars) with error bars representing standard error. Numbers in each bar
represent the number of sequences used to estimate momentum and are the same
for both parallel (A) and perpendicular (B) estimates. The bar labeled `All
jets' represents the sum of the mean momentum values for each body jet and the
dorsal and anal fin jets. Momentum is scaled to the fish's momentum M
at the end of stage two. (A) Momentum parallel to the final fish trajectory.
The bars for jet three are shown offset from one another to indicate that
parallel momentum in that jet decreased from stage one to stage two. (B)
Momentum perpendicular to the final fish trajectory. Note that the
perpendicular fish momentum at the end of stage two is zero by definition
explaining why no open bar is shown.
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Fig. 9. The force that produced jet two (i.e. the change in jet two momentum)
typically had two peaks, one in stage one and another in stage two. (A)
Example force trace showing the two peaks, identified with open circles. Stage
one and two are separated by dotted lines. Outlines showing body conformation
during the C-start are shown in the middle of the graph. The mean force
required to give the fish its final momentum is shown as a broken line. Time
zero is the time of first visible movement. (B) Mean values of the stage one
and two peak forces (open circles in A) for all trials. Force has been
normalized by the mean force (broken line in A) for each trial.
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Fig. 10. Summary of jet and fish momentum for body trials. Jets are shown in blue;
each line represents the magnitude and angle of a jet, radiating from the mean
position of the jet. Mean angle and momentum is shown with a black arrow. Fish
momentum is shown in a similar way with red lines radiating from the fish's
center of mass and a black arrow to indicate the mean. Fish silhouettes are
shown in gray. All vectors are scaled as a fraction of the final fish momentum
at the end of stage two (E). Data are for body jets, as indicated by the
inset.
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Fig. 11. Fluid momentum perpendicular to the fish's final trajectory reduces the
fish's total momentum. The fish momentum at the end of stage two is plotted
against the fraction of perpendicular jet momentum in the total momentum.
Mjet,i is the perpendicular
component of jet momentum, and the operators max(·) and
||·|| indicate the maximum value over time and the vector
magnitude, respectively.
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© The Company of Biologists Ltd 2008
