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Locomotion in scombrid fishes: visualization of flow around the caudal peduncle and finlets of the chub mackerel Scomber japonicus

Jennifer C. Nauen^* and George V. Lauder

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

View larger version (91K): [in a new window]   Fig. 1. Dorsal (x, z axes, viewed using a mirror, upper panels) and lateral (y, x axes, lower panels) views of the trailing (A) and leading (B) surfaces of finlets 4 and 5 and the caudal peduncle of a mackerel 22 cm in fork length (FL) during the deceleratory phase of a stroke at a steady swimming speed of 1.2FLs-1. The dorsal and lateral views are synchronous; time is shown in the lower field only. The outer finlet margin is outlined with the filled line; the circle indicates the anterior attachment point of each finlet. The finlets oscillate from the left (A) to the right (B) side of the dorsal and ventral body midlines (dotted lines) during the stroke and reach maximum excursions (note the tips of dorsal and ventral finlets 5 touching at the lateral midline of the body in the lower panel of A) on the trailing surface of the peduncle as the peduncle decelerates (the case shown in A is the left surface of the peduncle as it decelerates to the right). Scale bars (white lines) represent 1 cm; white arrows show the direction of tail movement.

View larger version (99K): [in a new window]   Fig. 2. Lateral view of the trailing surface of the caudal peduncle [A, note that the tips of the dorsal and ventral fifth finlets meet at the lateral body midline (a) on the trailing surface of the caudal peduncle] and the leading surface of the peduncle (B, note that the finlets are not visible along the peduncle) of a 24 cm fork length (FL) mackerel during the deceleration phase of the stroke at a steady swimming speed of 1.2FLs-1. The flow is seeded with reflective glass beads and illuminated by a vertically oriented laser light sheet. Velocity vectors in yellow were calculated using digital particle image velocimetry (DPIV) (see Materials and methods). Scale bars (white, lower left) represent 1 cm; scale arrows (white, lower left) represent a flow speed of 25 cms-1. ß, particle trajectory angle. Values are means ± S.D.

View larger version (37K): [in a new window]   Fig. 3. Lateral view of particle tracks along the trailing (A, finlets present, gray particle tracks) and leading (B, finlets absent, black particle tracks) surface of the caudal peduncle and caudal fin (outlined in blue) as the peduncle decelerates during steady swimming at 1.2FLs-1, where FL is fork length. The caudal keels (blue lines) are shown on the lateral surface of the caudal fin. These particles were digitized from four consecutive tail strokes by a mackerel 24 cm in fork length. Each track represents the movement of a single particle; each arrow represents the distance traveled by that particle in 4ms. Particle tracks along the finlets and caudal peduncle (within the dotted lines in A) were compared with the tracks of particles above and below the finlets and peduncle (within the solid lines in A) to describe flow in the region of and adjacent to the finlets and to test hypotheses about finlet function.

View larger version (34K): [in a new window]   Fig. 4. Particle trajectory along the trailing (gray circles, finlets present) and leading (black circles, finlets absent) lateral surfaces of the caudal peduncle as a function of the vertical position of the particle on the body (A) for all four mackerel examined. Each symbol represents a single particle; mean trajectory and position (N=3 or more) for each particle are plotted here. The lines represent the linear regression models fitted to the data sets. Note that the abscissa of this panel indicates the position of each point relative to the y axis (see Fig.1), with positive and negative values indicating dorsal and ventral locations relative to the horizontal midline, respectively. The ordinate indicates the angular trajectory of each particle track. These data are summarized graphically in B, in which a lateral view of the caudal peduncle (gray dashed lines), finlets 4 and 5 (gray solid lines), the lateral body midline (black dotted line) and the caudal keels (black lines) is depicted. Average values of flow trajectory (arrows) along the caudal peduncles and finlets and above and below these structures are shown on the trailing (gray arrows) and leading (black arrows) surface of the peduncle.

View larger version (71K): [in a new window]   Fig. 5. Ventral view of a 26 cm fork length (FL) mackerel swimming at 1.2FLs-1 illuminated by a laser light sheet oriented in the horizontal (xz) plane. The peduncle and caudal fin are beginning to decelerate to the right (direction indicated by white arrow). The ventral margin of finlet 5 is outlined by the black line; its anterior attachment point is indicated by the black circle. Flow vectors were calculated using digital particle image velocimetry (DPIV); mean values of flow trajectory (ß) indicate the formation of cross-peduncular flow on the right side of the mackerel and longitudinal flow on the left side of the mackerel. Values are means ± S.D. The scale bar (white, lower left) represents 1 cm (note that only the posterior fifth of the body is seen in the field of view); the scale arrow (white, lower left) represents a flow of 25 cms-1.

View larger version (68K): [in a new window]   Fig. 6. The position of two particles (highlighted by the green and orange open circles) are tracked through a time series of images (A–D) showing the ventral view of a 26 cm fork length (FL) mackerel swimming at 1.2FLs-1 as the peduncle declerates to the right (direction of movement indicated by the white arrow). The ventral surface of the mackerel and reflective particles in the water are illuminated by a laser light sheet oriented in the horizontal plane. The ventral margin of the fifth finlet is highlighted by the black line. The scale bar (white line, lower left of C) represents 1 cm. (E–H) Diagrams presenting hypothetical lift (FL, green arrows), drag (FD, red arrows) and resultant forces (FR, gray arrows) created by the interaction between a finlet (solid black lines) and the local flow (solid blue lines) of varying trajectories. The orientations of the finlet and flow with respect to the horizontal are indicated by dotted black and blue lines, respectively. Note that thrust, which in these cases is produced when the resultant vector is angled to the left, is created only if the angle between the finlet and the horizontal is less than that of the local flow (E and H). Data shown in A–D correspond to the theoretical diagram in F, in which no thrust is generated.

View larger version (26K): [in a new window]   Fig. 7. A time series of the angle of finlet 5 (f5; black symbols) and the angles of various particles (each particle in a stroke is represented by a different colored symbol) with respect to the horizontal (left y axis) over a series of five strokes. The oscillation of the body of the 24 cm mackerel swimming at 1.2FLs-1, where FL is fork length, is represented by the position of the body at the insertion of finlet 5 on the z axis (gray symbols, right y axis). Particles were digitized over the second half of each stroke (at times highlighted by the gray boxes), during which time the peduncle and caudal fin decelerate (Nauen and Lauder, 2000). Note that the particle trajectory angles are not equal to the orientation angle of finlet 5 over a series of strokes, indicating that finlet 5 is at an angle of attack to the local flow and that the finlet is typically oriented at a steeper angle to the horizontal than is the local flow, indicating that no thrust is produced (see Fig.6F,G).

View larger version (17K): [in a new window]   Fig. 8. Particle trajectory angle as a function of the angle of finlet 5. Each symbol represents the mean angle (N=3 or more) for a single particle. The broken line represents a 1:1 relationship. The solid line represents the least-squares linear regression relationship fitted to the mean data.

View larger version (16K): [in a new window]   Fig. 9. Schematic lateral view of the left side of a chub mackerel in which the body is outlined in gray and the finlets and caudal keels are outlined in black. Idealized flow trajectories (gray arrows) are shown for forward gliding (A, body motion indicated by the black arrow), in which there is no lateral movement of the caudal peduncle or finlets, and for lateral movement of the body without forward movement (B, body motion indicated by the black arrow). Forward gliding without lateral movement (A) is expected to create convergent flow along the peduncle. Lateral movement of the peduncle without forward movement (B) is expected to create divergent flow on the leading surface of the peduncle and convergent flow on the trailing surface. The observed flow pattern on a steadily swimming mackerel is a combination of these two idealized patterns. Above the lateral midline of the fish on the leading peduncular surface (shown), the downward trajectory of flow above the horizontal expected under A sums with the upward trajectory expected under B to result in essentially horizontal flow. The downward trajectory of flow on the trailing peduncular surface expected under A sums with the downward trajectory expected under B to result in flow above the horizontal moving towards the midline on the trailing surface. Flow below the horizontal follows the opposite pattern.