Routine turning maneuvers of koi carp Cyprinus carpio koi: effects of turning rate on kinematics and hydrodynamics

SUMMARY Spontaneous swimming behaviors of koi carp Cyprinus carpio koi were recorded using a video tracking system. Routine single-beat turns were selected from the recorded image sequences for kinematic and hydrodynamic analysis. As with C-starts, the turns can be divided into two stages (stage 1 and stage 2), based on kinematics. Stage 1 involves a bend to one side forming a C-shaped curve in the body, while stage 2 corresponds to the return flip of the body and tail. The turning angle in stage 1 accounts for the greatest portion of the total turning angle and the mean turning rate in stage 1 reflects the intensity of turn. The effects of the turning rate in stage 1 on both kinematics and hydrodynamics were examined. The duration of stage 1 remained relatively stable over a nearly tenfold change in turning rate. Consequently, the turning angle is dominated by the turning rate in stage 1. The turning radius is not related to the swimming speed. Moreover, except in very fast turns, the turning radius is also not affected by the turning rate. The angle between the side jet and the carp's initial orientation of a turn does not change substantially with the turning rate, and it is always close to 90° (94.2±3.1°, N=41), so the orientation of the side jet in the forthcoming turn can be predicted. The angle between the jet and the line joining the center of mass of the carp and the trailing edge of the tail (mean value in stage 1) is also always close to 90° (95.3±1.3°, N=41). It is helpful for the carp to maximize the torque so as to improve the turning efficiency. In stage 1, the impulsive moment obtained from the beat of the body and tail and the mean angular momentum of the carp show an agreement in magnitude. Two types of flow patterns in the wake of routine single-beat turns are revealed. The difference between the two types of wakes is in whether or not a vortex ring and a thrust jet are generated in stage 2. The recoil speed of the tail, the bending amplitude of the turn, and the angle of attack of the tail are three probable factors influencing the flow patterns in stage 2.