Why Does Fish Escape So Fast?
The significant effects of a travelling curvature wave in the flow control of a C-start motion
Yu, Yongliang etc.
C-Start without travelling curvature wave C-start with travelling curvature wave

C-start is a kind of fast-start motion usually observed in fish’s escape responses with their body bending into the shape of the letter ‘C’ and then flapping back to escape predators. It is a sudden maneuvering motion which comprises not only fast turning but also high speed escaping. Previous observers showed that fish can achieve a turn angle from 0 to 180° on left or right side of their bodies in C-starts. The peak acceleration rate in this kind of motions may exceed 10 times of the gravity acceleration rate, so that fish can get a high escaping speed in a short time. Due to such an excellent maneuverability presented, C-start attracted many attentions in the past.

The C-start kinematic characteristics for different fish species has been reviewed by Domenici and Blake. A lot of studies on swimming mechanisms of C-start have also been carried out, e.g. the estimation of the hydrodynamic forces, the theoretical analysis of the power output and the propulsive efficiency, the model or vivo experiments on the hydrodynamics and the mechanism of the thrust production.

From a dynamic standpoint, a fish flexes its body in the water, obtaining the reactive forces at the same time, and then starts to move due to the hydrodynamic driving forces. How does the fish body’s bending process lead to the excellent maneuverability during C-start?

According to the observation, a typical C-start deforming mode actually includes two parts, i.e. (1) a ‘C’ shape bending and a return flapping which can be assumed as a standing bending wave and (2) a rearward travelling curvature wave. Most previous studies paid more attention to the former, but seldom discussed the dynamical effects of the latter. Can the travelling curvature wave be neglected? If not, what role does it play during a C-start?

In the Laboratory for Biomechanics of Animal Locomotion, the escaping performance of fishlike C-start motions has been numerically investigated for the flow physics study by use of a two-dimensional deformable foil bending and stretching quickly. We found that if proper values of the travelling curvature wave parameters are chosen, the fish’s C-shape escaping maneuverability presented with traveling wave is much better than that without it, i.e. the turn angle and the speed of the center of mass (COM) at the end of a C-start in IM is almost twice as large as those in BM. Further study shows that the travelling curvature wave not only can enhance the thrust and the centripetal force but also increase the propulsive efficiency. These results suggest that an efficient travelling curvature wave is of great significance in the flow control of a C-start motion. Finally, a parametric study finds that the phase difference between the ‘C’ shape bending and the travelling curvature wave (i.e. the initial phase angle in travelling curvature wave of the deforming model) is a key parameter in the flow control. To achieve the desirable turn angle, escaping speed and propulsive efficiency in the C-start motions, the initial phase angles must be ranged within specific magnitudes. It is found that for optimum values of the initial phase angle, the foil’s flexible deforming process is qualitatively consistent with that of a fish body in nature. The results obtained in this study provide a new physical insight into the understanding of swimming mechanisms of fish’s C-start maneuvers.

The above results have been published in Physical Review E (2011).