Liu Geng, Yu Yong-Liang, Tong Bing-Gang
The Laboratory for Biomechanics of Animal Locomotion, the Graduate University of the Chinese Academy of Sciences, 100049 Beijing, People's Republic of China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Nov;84(5 Pt 2):056312. doi: 10.1103/PhysRevE.84.056312. Epub 2011 Nov 18.
Fish usually bend their bodies into a ''C'' shape and then beat their tails one or more times to escape from predators (in nature) or stimuli (in experiments). The maneuvering behavior, i.e., the C-shape bending and the return flapping, is called C-start. In this paper, the escaping performance of fishlike C-start motions has been numerically investigated for a flow physics study by the use of a two-dimensional deformable foil bending and stretching quickly. The C-start motions, performed in the quiescent water and based on prescribed deforming modes, are predicted by a numerical method coupling the two-dimensional incompressible Navier-Stokes equations and the deforming body dynamic equations. It has been found earlier that a typical C-start motion consists of (1) a main C-shape bending and (2) a rearward travelling curvature wave which was seldom mentioned in previous studies. In order to reveal the flow control mechanism of the traveling curvature wave in a fish's C-start motion, two kinds of C-start flows with different deforming modes, namely the integrated mode (IM, a C-shape bending plus a travelling curvature wave) and the basic mode (BM, a C-shape bending only) are analyzed and compared in detail. According to the numerical results, it shows that if proper values of the travelling curvature wave parameters are chosen, the foil's escaping maneuverability presented in the IM is much better than that in the BM, i.e. the turn angle and the speed of the center of mass at the end of a C-start in the IM is almost twice as large as those in the 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 the 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.
鱼类通常会将身体弯曲成“C”形，然后快速摆动尾巴一次或多次，以逃避天敌（在自然环境中）或刺激（在实验中）。这种机动行为，即C形弯曲和回摆动作，被称为C型启动。在本文中，为了进行流动物理学研究，通过使用快速弯曲和拉伸的二维可变形箔片，对类鱼C型启动运动的逃逸性能进行了数值研究。在静止水中基于规定变形模式执行的C型启动运动，是通过将二维不可压缩纳维-斯托克斯方程与变形体动力学方程耦合的数值方法来预测的。较早前已经发现，典型的C型启动运动包括（1）一次主要的C形弯曲和（2）一个向后传播的曲率波，而这在以前的研究中很少被提及。为了揭示鱼类C型启动运动中传播曲率波的流动控制机制，详细分析和比较了两种具有不同变形模式的C型启动流，即综合模式（IM，C形弯曲加传播曲率波）和基本模式（BM，仅C形弯曲）。根据数值结果，结果表明，如果选择适当的传播曲率波参数值，IM中箔片的逃逸机动性比BM中的要好得多，即IM中C型启动结束时的转弯角度和质心速度几乎是BM中的两倍。进一步的研究表明，传播曲率波不仅可以增强推力和向心力，还可以提高推进效率。这些结果表明，有效的传播曲率波在C型启动运动的流动控制中具有重要意义。最后，一项参数研究发现，C形弯曲和传播曲率波之间的相位差（即变形模型传播曲率波中的初始相位角）是流动控制中的一个关键参数。为了在C型启动运动中实现理想的转弯角度、逃逸速度和推进效率，初始相位角必须在特定范围内。研究发现，对于初始相位角的最佳值，箔片的柔性变形过程在定性上与自然界中鱼体的变形过程一致。本研究获得的结果为理解鱼类C型启动机动的游泳机制提供了新的物理见解。
