JEB desktop wallpaper calendar 2016

JEB desktop wallpaper calendar 2016

Median fin function in bluegill sunfish Lepomis macrochirus: streamwise vortex structure during steady swimming
Eric D. Tytell
  1. Fig. 1.

    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 lines.

  2. Fig. 2.

    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.

  3. Fig. 3.

    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.

  4. Fig. 4.

    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.

  5. Fig. 5.

    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.

  6. Fig. 6.

    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 zL; thin black line, caudal fin tip vortex (upper vortex in A), at zL. 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.

  7. Fig. 7.

    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.

  8. Fig. 8.

    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.

  9. Fig. 9.

    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.

  10. Fig. 10.

    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.

  11. Fig. 11.

    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.

  12. Fig. 12.

    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.