Filming arrangement. (A) Flow tank filming configuration seen from above.
Two cameras film the fish from behind through a front-surface mirror at
45° in the flow downstream of the fish. The mirror, fish, and camera
positions are approximately to scale relative to the flow tank width. A laser
light sheet is projected in from the side. One camera views the sheet
orthogonally; the other is at a 12° angle. The off-axis camera uses a
Scheimpflüg lens mount to tilt the axis of the lens and focus on the
entire light sheet, despite the camera's angle. The x axis is
lateral, from the fish's left to right, and the z axis is streamwise
in the flow direction. (B) Side view of the filming configuration, showing the
ventral view camera used for kinematic measurements. PIV cameras are omitted.
The y axis is dorso-ventral and the z axis is streamwise.
(C) Sample image from the orthogonal PIV view. (D) Sample image from the
ventral view. (E) Terminology for regions in which streamwise vortices are
shed. Sources of vortices along the body are indicated by thick colored
Number of tail beats collected at different positions along the fish body
(L) for four individuals. Individuals are shown as different colors.
An image of a fish is shown in the background, scaled appropriately.
Tips of the caudal, dorsal and anal fins cup actively into the flow. Motion
of fins through half a tail beat from left to right in two transverse planes
is presented. Each panel shows 7 tracings of the posterior margins of the
fins, spaced equally in time, as seen from behind the fish. Color and
thickness of the bar indicate lateral velocity of a particular segment of the
fin. The beat frequency for each fin is the same, 4.9±0.3 Hz. (A)
Caudal fin kinematics. Note how the upper and lower lobes bend into the flow
at stroke reversal. Inset shows position of the two planes. (B) Dorsal and
anal fin kinematics. Note the cupping motion of the outer edges of each fin.
Scale bars are the same for A and B.
Examples of each of the ten different vortices identified. All images have
the original PIV image in the background, yellow vectors represent the flow
field, and vorticity is shown as colored contours. In all panels, scale bars
are 5 mm and scale vectors are 5 cm s–1. The heads of vectors
shorter than 3 cm s–1 are retained to indicate direction. (A)
Flow field at the posterior margin of the caudal fin, with the laser
illuminating the upper and lower lobes of the fin. The tail is moving from
left to right and has just formed the two tip vortices, labeled `caudal fin
(upper)' and `caudal fin (lower)'. Weak remnants of the outer dorsal and anal
fin vortices are still present, labeled `dorsal fin' and `anal fin'. The notch
between the two lobes of the caudal fin also sheds vortices, labeled `caudal
notch (upper)' and `caudal notch (lower)'. Every other vector is shown. (B)
Flow field at the trailing edge of the dorsal and anal fins, with the laser
illuminating the two fins and part of the caudal peduncle. The caudal fin
blocks the view of some of the flow field. The fins are finishing motion from
left to right, and the peduncle has just begun to move from right to left.
Outer vortices from the dorsal and anal fins are fully developed (labeled
`dorsal fin' and `anal fin'). The fins have also formed vortices on their
inner edges, labeled `dorsal fin (inner edge)' and `anal fin (inner edge)'.
Two vortices may have been shed from the peduncle (both labeled `peduncle?'),
but it is difficult to be certain because of the shadow cast by the peduncle.
(C–E) Insets showing details of the vector fields boxed in A and B. All
vectors are shown in these panels.
Pseudo-three-dimensional view of the wake, showing the x and
y positions of vortices detected at the tip of the caudal fin, with
time as the third axis. This view is representative of the streamwise vortices
in the wake if the vortices did not evolve over time or interact with each
other. The sheet swept out by the caudal fin is shown in gray. Identified
vortices are colored by circulation, while vortices that were detected but
whose source could not be determined are shown with shades of gray
representing circulation. Vortices shed by the caudal fin, including the two
tip vortices and the caudal notch vortices, have a black mesh, while the outer
dorsal and anal fin vortices have a white mesh.
Identification of outer dorsal fin vortex in the wake. (A) Two vortices
above the upper margin of the caudal fin in a plane approximately 5 mm
downstream of the tail, shown by a thick black line. The caudal fin vortex
appeared first and is clearly a tip vortex from the caudal fin. The lower
vortex, labeled `dorsal fin vortex', appears later. (B) Plot of the
circulations of three vortices against tail beat phase. Red line, outer dorsal
fin vortex as it is formed on the dorsal fin at z≈0.7L;
broken blue line, lower vortex in (A) at z≈L; thin black
line, caudal fin tip vortex (upper vortex in A), at z≈L.
Black bars indicate the length of time it would take flow to pass from the
posterior margin of the dorsal fin to the tip of the tail, positively
identifying the blue trace as the outer dorsal fin vortex. Dotted vertical
line indicates the time of A.
Mean vortex circulation changes along the body. All plots have the same
x axis: body position in L. (A) Example of raw data used for
the vortex circulation. Peak positive and negative circulation for the dorsal
fin vortex are shown. Color indicates circulation magnitude (mag.); squares
and diamonds are from positive and negative circulation vortices,
respectively. Broken and dotted lines indicate flow speed and wave speed,
respectively, and are spaced 50% of the tail beat cycle apart. (B,C) Results
of the regression of circulation on phase and body position, detailed in Eqn
4, showing the amplitude of the oscillation in circulation (B) and the phase
of the positive circulation peak (C). Line color indicates specific vortices,
shown schematically at the bottom of B. Phase trajectories in C that wrap
around from 100% back to 0% are indicated with arrowheads and -tails. Although
the regression from Eqn 4 is linear in the amplitude of the sine and cosine
terms separately, the joint amplitudes and phases can have nonlinearities due
to the differing weights of the coefficients. See text for more details.
Sum of the regressions for each individual vortex's circulation to
determine how total circulation changes as flow moves down the body. Broken
lines on each plot indicate the slope of the flow speed; they are only visual
guides and are not fit to the data. (A) Total circulation magnitude along the
body over the tail beat cycle, composed of the smoothed sum of the fitted
circulations for each identified vortex. (B) Magnitude of circulation added
per unit length by each position on the body over half of a tail beat cycle,
estimated by taking the derivative of A with respect to position along the
broken lines of flow speed. The zero contour is outlined in a thin solid black
line, indicating that circulation is removed at certain times and places.
Averaged over a tail beat, circulation increases at the dorsal and anal
fins and at the trailing edge of the caudal fin, but decreases at the caudal
peduncle and base of the caudal fin. Bars show mean circulation added over a
tail beat at 12 points along the body, each 0.025L wide.
The dorsal and anal fins produce vortices with streamwise circulation
statistically indistinguishable from those produced by the caudal fin. Bars
show the mean + s.e. of the peak circulation over the entire body, based on
the ANOVA described in the text. Vortices with circulations that do not differ
significantly (P<0.05) are connected by bars below the plot. Inset
shows the position on the body where each vortex was generated.
Representative plot of the geometric effectiveness E measured at
0.95L, with example flow fields at approximately 25% and 75% through
the tail beat cycle. (A,B). Example flow fields showing the main flow patterns
as the tail moves from left to right (A) and from right to left (B). The tail
is shown in blue. Scale bars and scale vectors shown below the panels are
valid for both. Light passes through the tail to a small extent, allowing the
estimation of some vectors in the shadowed (right) side, but these vectors,
shown in gray, were not used in the effectiveness calculations. (C)
Effectiveness estimated assuming tail beats are symmetrical (red line) by
using the previous half tail beat to reconstruct flow in the shadowed side of
the tail. The black line shows the single-side effectiveness, using only the
flow on the illuminated side of the tail. Single-side effectiveness is higher
in the first half of the tail beat, showing that the tail is less effective at
sucking fluid laterally than it is at pushing it, probably due to its cupped
shape. The dotted lines show the times at which A and B were measured.
Proposed 3D vortex structure around a swimming bluegill sunfish. Vortex
loops are shed off the caudal, dorsal and anal fins, shown in green, red and
blue, respectively. Vortex filaments and their directions are shown by solid
arrowheads. The direction of vortex rotation, derived by the right hand rule
from the filament direction, is shown with open arrowheads where there is
space. (A) 3D view, showing the proposed linkages between caudal fin tip
vortices and dorsal and anal fin vortices. Question marks are shown where the
connection between dorsal or anal fin vortices and the caudal fin wake is
unclear. The notch vortices in the far wake are shown by dotted lines,
indicating that the structure is hydrodynamically unstable and may not persist
in the form shown. A projection of the vortex structure in the horizontal
plane is shown below, with dotted lines indicating the correspondence between
the projection and four centers of rotation. Note that the projection is taken
from multiple horizontal planes. A midline tracing, in the correct phase, is
shown below the fish. (B) Side views of the vortex filaments shown in A as the
fish swims from left to right, showing how the dorsal and anal fin vortex
filaments could potentially join up to the caudal fin vortices. Notch vortices
in the far wake are again shown dotted to indicate their instability. (C)
Schematic of the progression of the outer dorsal fin vortex and its
interaction with the caudal fin, shown at three points in time from top to
bottom. The fish is holding station in flow moving from right to left. L, low
pressure zones that would be formed along the tail due to the proximity of the
outer dorsal fin vortex.