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Hydrodynamics of caudal fin locomotion by chub mackerel, Scomber japonicus (Scombridae)

Jennifer C. Nauen^* and George V. Lauder

Department of Organismic and Evolutionary Biology, Harvard University, 26 Oxford Street, Cambridge, MA 02138, USA

View larger version (83K): [in a new window]   Fig. 1. Mackerel swam at a constant speed of 1.2 or 2.2 FLs-1, where FL is fork length, in a flow tank, and a laser light sheet oriented in the vertical (parasagittal, XY) (shown) or horizontal (frontal, XZ) plane illuminated small particles in the flow. Camera 1 recorded images of the caudal fin and the area of the light sheet posterior to it; in the example shown in A, the tail is beating out of the plane of the light sheet towards the reader with the caudal fin tilted at an acute angle to the Y axis (as also shown by Gibb et al., 1999). The ventral lobe of the caudal fin, illuminated by the light sheet, is trailing the dorsal lobe, which has previously passed through the sheet. Camera 2 recorded synchronous images of the body of the mackerel that were used to determine the orientation of the body to the X axis. Images of the light sheet oriented in the XZ plane (B) were recorded from below the tank using a front-surface mirror. Note that the caudal peduncle and fin blocked the light sheet as they moved through it (the arrow in B indicates the direction of fin movement), creating a shadow (seen, for example, in B). Yellow dotted lines in A and B outline the approximate image area analyzed using digital particle image velocimetry. The white scale bars in the lower left of A and B represent 1 cm.

View larger version (82K): [in a new window]   Fig. 2. The time course of vortex production over approximately one tail beat of a Scomber japonicus 24 cm in fork length (FL) swimming at 1.2 FLs-1. The distal tips of the caudal fin were positioned approximately 1 cm to the left of the flow fields shown (see Fig. 1B for an example of caudal fin position and image region analyzed). The caudal fin was moving through the horizontal (XZ) light sheet at the position of the fin's lateral midline (as confirmed by camera 2, see Fig. 1, and shown in the diagram of the caudal fin and light sheet). Fin position relative to the Z axis was determined at 4 ms time intervals. Arrows in the time series indicate times at which a vortex could first be seen distinct from the caudal fin; gray columns indicate the time of the wake images presented below. Flow velocity is represented by the black vectors plotted over a color background indicating flow vorticity. Vortices in the wake are numbered consecutively in the order in which they are shed from the caudal fin. V2, V3, vortices 2 and 3. Note that the vortex number is placed approximately in the center of the vortex (as defined by vector orientation), which does not necessarily correspond with the area of highest vorticity (i.e. the region of most intense red or blue color).

View larger version (86K): [in a new window]   Fig. 4. Views of the wake in the vertical (XY) plane of an individual of Scomber japonicus 26 cm in fork length swimming steadily at speeds of 1.2 FLs-1 (A) and 2.2 FLs-1, where FL is fork length (B). The orientation of the caudal fin to the light sheet is shown in the diagram. Flow velocity is represented by black vectors plotted over a color background indicating vorticity. At both swimming speeds, the caudal fin sheds one pair of counter-rotating vortices with a central jet of high-velocity flow per stroke. The white arrows and labels in B illustrate the axes of velocity profiles presented in Fig. 5. X' is the longitudinal axis of the ring; Y' is perpendicular to X'.

View larger version (23K): [in a new window]   Fig. 6. Jet angle as a function of ring axis angle. Diagrams indicate jet () and ring axis (ß) angle relative to the X axis as defined for vortices viewed with a horizontal (top diagram) and a vertical (bottom diagram) light sheet. Note that is not shown in the vertical sheet diagram because jet angle relative to the X axis is 0°. Viewed in the XZ plane (horizontal light-sheet data, circles) at 1.2 FL s-1 (open symbols) or 2.2 FL s-1 (filled symbols), the angle of the jet flow to the X axis was always less than 90° (upper dotted line), indicating a thrust component to the jet. Viewed in the XY plane (vertical light-sheet data, squares), jet orientation was typically slightly negative relative to the X axis (lower dotted line) over a range of ring axis angles of more than 40°. FL, fork length.

View larger version (18K): [in a new window]   Fig. 7. Ring axis angle (circles) and jet angle (squares) relative to body angle to the X axis at swimming speeds of 1.2 FL s-1 (open symbols) and 2.2 FL s-1 (filled symbols). All measurements were made in the vertical (XY) plane. FL, fork length.

View larger version (74K): [in a new window]   Fig. 3. Views in the horizontal (XZ) plane of the wake of a Scomber japonicus, 24 cm in fork length, swimming steadily at 1.2 FLs-1, where FL is fork length. Flow velocity is represented by black vectors plotted over a color background indicating vorticity. (A) Only low levels of vorticity (green) are present in the horizontal plane of fluid just above the caudal fin, as seen when the dorsal tip of the tail just intersects the sheet (indicated by the schematic view of the caudal fin relative to the light sheet to the left of each plot). Relatively strong negative and positive vorticity, associated with counterclockwise and clockwise vortices, respectively, and a broad central jet of flow are seen when the middle of the tail's upper lobe intersects the light sheet (B) and when the light sheet is at the lateral midline of the tail (C). One vortex ring is shed during each stroke of the caudal fin.

View larger version (23K): [in a new window]   Fig. 5. Comparison of theoretically predicted velocity profiles across planar sections of isolated vortex rings (left panels, where paired circles indicate vortex cores in solid-body rotation and arrows indicate the direction of induced flow rotation; Milne-Thompson, 1966) with velocity profiles taken from XY planar light-sheet images of the wake of a mackerel 26 cm (fork length, FL) swimming at 1.2 FL s-1 (right panels). The velocity values shown are raw data calculated using a high-resolution 50x50 vector field. (A) X' is the longitudinal axis of the vortex ring, which traverses the centers of the two vortex cores; (B) Y' is the central axis of a vortex ring (perpendicular to X'); (C) Y' is the line extending across the counterclockwise vortex core parallel to the ring's central axis (see Fig. 4B for an illustration of axes used here on an XY planar vorticity plot). The components of velocity parallel to X' and Y' are u' and v', respectively. In the region of the central jet, v' is negative.

View larger version (17K): [in a new window]   Fig. 8. Summary of the empirically determined hydrodynamic forces created by chub mackerel Scomber japonicus swimming steadily at 1.2 FL s-1. Flow fields and forces are depicted in the vertical (XY, top) and horizontal (XZ, bottom) planes. Vortex rings are shown in blue; ring dimensions and orientation represent those determined empirically in this paper (Table 1). Thick black arrows represent central jet flow. Red arrows represent the reaction force on the caudal fin; in the vertical plane, reaction force is directed behind the body, so the red arrow is broken. Thrust, lift and lateral force values are the mean reaction forces averaged over a stroke period. S. japonicus swims with its body slightly tilted down (-3° on average); the jet is tilted down -3° in the opposite direction. Thus, the reacion force at the caudal fin has a lift component that acts over the lever arm of body length to the center of mass (black-and-white checkered circle) to rotate the head down (green arrow). Lift generated by abducted pectoral fins (P), such as has been observed in previous kinematic studies, could counterbalance lift generated at the caudal fin.