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First published online July 25, 2005
Journal of Experimental Biology 208, 2939-2949 (2005)
Published by The Company of Biologists 2005
doi: 10.1242/jeb.01733

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Aquatic wing flapping at low Reynolds numbers: swimming kinematics of the Antarctic pteropod, Clione antarctica

Brendan J. Borrell^1,*, Jeremy A. Goldbogen¹ and Robert Dudley^1,2

¹ Department of Integrative Biology, University of California, Berkeley, CA 94720, USA
² Smithsonian Tropical Research Institute, P.O. Box 2072, Balboa, Republic of Panama

View larger version (22K): [in a new window]   Fig. 1. Wingtip motion for a Clione antarctica during a single wingbeat cycle (a–i) from lateral (above) and dorsal (below) perspectives. Mean relative velocity of the body (blue arrows) and mean body acceleration vectors (red arrows) are averaged from data for eight individuals. The external coordinate system is shown indicating the x-, y- and z-axes. The body coordinate system is indicated by the y'- and z'-axes, but, in this example, the x'-axis is not shown because it is coincident with the x-axis. The origin of the body coordinate system is at the near wing base.

View larger version (42K): [in a new window]   Fig. 2. (A) Right lateral and dorsal views of wingtip displacement relative to the wing base for Clione antarctica (individual no. 1) swimming at 0.3°C. (B) Wingtip position vs time for two wingbeat cycles. Circles represent the position of digitized data points, and plotted lines are spline functions fitted to time series data. P, posterior; A, anterior; D, dorsal; V, ventral; R, right; L, left.

View larger version (25K): [in a new window]   Fig. 3. Relative wingtip position and relative body angle during a complete wingbeat cycle for Clione antarctica. Thin lines are interpolated points from a spline function fitted to digitized kinematic data from individual sequences. Thick red lines represent the mean value for all kinematic sequences. P, posterior; A, anterior; D, dorsal; V, ventral; R, right; L, left.

View larger version (17K): [in a new window]   Fig. 4. Kinematic parameters as a function of non-dimensional body velocity in Clione antarctica. (A) Angle of attack () increases with non-dimensional velocity (r2=0.741, F1,6=17.155, P=0.0061); (B) stroke plane angle during the power phase (ßps) increases with non-dimensional velocity (r2=0.725, F1,6=15.780, P=0.0073); (C) angle of ascent during the power phase (ps) increases with non-dimensional velocity (r2=0.701, F1,6=14.099, P=0.0095); (D) kinematic definitions of angle of attack, stroke plane angle during the power phase, and ascent angle.

View larger version (11K): [in a new window]   Fig. 5. Lateral projection of the geometric center of area of a Clione antarctica (individual no. 1) in vertical ascent during two complete wingbeat cycles. Arrows denote: a, the beginning of the power phase of the upstroke; b, recovery phase of the upstroke; c, power phase of downstroke; d, recovery phase of the downstroke; and e, the end of the stroke cycle.

View larger version (27K): [in a new window]   Fig. 6. Fore–aft acceleration of the body in relation to three wingtip variables: fore–aft velocity, fore–aft acceleration, and transverse (lateral and dorsoventral components) velocity. Thin lines are estimated from the second derivative of a spline function fitted to the digitized kinematics from individual sequences. Thick lines represent mean values averaged across all eight sequences.

View larger version (12K): [in a new window]   Fig. 7. Timing of kinematic events in relation to fore–aft accelerations of the body based on data from eight Clione individuals as shown in Fig. 6. Inflection points not unambiguously identified were excluded from the analysis. The central line indicates the median value, the grey box delimits the upper and lower quartiles, and whiskers indicate the range of the remaining data.

View larger version (30K): [in a new window]   Fig. 8. Dorsoventral components of wingtip velocity and acceleration, and rotational acceleration of the body for ascending Clione antarctica. Thin lines are estimated from the first derivative of a spline function fitted to digitized kinematic data from individual sequences. Thick red lines represent the mean values averaged across all eight sequences.

View larger version (11K): [in a new window]   Fig. 9. Timing of kinematic events in relation to angular accelerations of the body based on data from the eight Clione individuals shown in Fig. 8. Inflection points not unambiguously identified were excluded from analysis. The central line indicates the median value, the grey box delimits the upper and lower quartiles, and whiskers indicate the range of the remaining data.