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First published online November 30, 2007
Journal of Experimental Biology 210, 4379-4389 (2007)
Published by The Company of Biologists 2007
doi: 10.1242/jeb.009787
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Routine turning maneuvers of koi carp Cyprinus carpio koi: effects of turning rate on kinematics and hydrodynamics

Guanhao Wu1,*, Yan Yang2,3 and Lijiang Zeng1

1 State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instruments, Tsinghua University, Beijing 100084, China
2 The Laboratory for Biomechanics of Animal Locomotion, Graduate University of Chinese Academy of Sciences, Beijing 100049, China
3 Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China


Figure 1
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  		Fig. 1. The coordinate system and notation used to describe the kinematics and the wake of the fish. Two counter-rotating circles represent a pair of vortices. The bold arrow indicates the jet flow. The dotted line indicates the body axis of the carp at the onset of a turn. The broken lines are auxiliary lines. See text for more details and List of symbols and abbreviations for definitions.

 

Figure 2
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  		Fig. 2. Frequency distributions of the routine single-beat turns in the four turning categories. Open bars, turns with type I wake; filled bars, turns with type II wake. The sum of the two bars represents the total number of turns in each category.

 

Figure 3
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  		Fig. 3. Mean turning rate in stage 1 ({omega}1) plotted against (A) the turning angle in stage 1 (β1), (B) the bending amplitude (dmax), (C) the moving speed at the onset of a turn (U0), (D) turning radius (Rt), (E) net change of speed in stage 1 ({Delta}U1) and (F) net change of speed in stage 2 ({Delta}U2). In A,B,E,F, linear regression lines are shown as solid lines (see text and Table 1 for regression coefficients and P values). No significant linear relationship exists in C and D and so a regression line is not shown.

 

Figure 4
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  		Fig. 4. Representative flow patterns of wake type I. Black arrows represent flow velocity magnitude and direction, and vortices are numbered. Vorticity is shown in color in the background. (A–F) Evolvement of vorticity and flow velocity vector fields at different times during the turn.

 

Figure 5
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  		Fig. 5. Representative flow patterns of wake type II. See legend of Fig. 4 for details.

 

Figure 6
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  		Fig. 6. Linear regressions of mean turning rate in stage 1 ({omega}1) plotted against (A) the momentum of the vortex ring (I1) and the jet angle in stage 1 ({alpha}1) and (B) the impulsive moment obtained from the beat of the body and tail (Li1) and the mean angular momentum (Lj1) in stage 1.

 

Figure 7
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  		Fig. 7. Linear regressions of mean turning rate in stage 1 ({omega}1) plotted against (A) the momentum of the vortex ring shed in stage 2 (I2) and (B) the jet angle of the vortex ring shed in stages 2 ({alpha}2).

 

Figure 8
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  		Fig. 8. (A) Scatter plot of the recoil speed of the tail in stage 2 against the mean turning rate in stage 1 ({omega}1). Filled circles, turns with type I wake; open circles, turns with type II wake. (B) Scatter plot of the momentum of the vortex ring shed in stage 2 (I2) against the recoil speed of the tail in stage 2. (C) Linear regression of I2 against the bending amplitude (dmax).

 




© The Company of Biologists Ltd 2007