Note on the swimming of an elongated body in a non-uniform flow
Note on the swimming of an elongated body in a non-uniform flow
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DOI：
10.1017/jfm.2012.560
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发表时间：
2013-02-01
影响因子：
3.7
通讯作者：
Boyer, Frederic
中科院分区：
文献类型：
--
作者：
Candelier, Fabien;Porez, Mathieu;Boyer, Frederic
本文提出了一个扩展的Lighthill的大振幅细长体理论的鱼类运动，使外部弱非均匀势流的影响被考虑在内。为此，将机身建模为基尔霍夫梁，该梁由椭圆形横截面组成，其尺寸可沿机身沿着变化，并经历由偏航和俯仰弯曲组成的规定变形。流体速度势被分解为两部分，对应于未扰动的势流，这是假设是已知的，和扰动流。控制扰动速度势的拉普拉斯方程和相应的诺依曼边界条件用曲线坐标表示，曲线坐标在物体运动过程中跟随物体，从而使物体的边界被认为是一个固定的表面。根据物体的细长性和无扰流不均匀性的弱点，对方程进行了简化。这些简化允许使用经典的伯努利方程分析确定作用在身体上的压力，然后对身体进行积分。最后利用该模型研究了卡门涡街中鱼的被动游动和主动游动。
This paper presents an extension of Lighthill's large-amplitude elongated-body theory of fish locomotion which enables the effects of an external weakly non-uniform potential flow to be taken into account. To do so, the body is modelled as a Kirchhoff beam, made up of elliptical cross-sections whose size may vary along the body, undergoing prescribed deformations consisting of yaw and pitch bending. The fluid velocity potential is decomposed into two parts corresponding to the unperturbed potential flow, which is assumed to be known, and to the perturbation flow. The Laplace equation and the corresponding Neumann's boundary conditions governing the perturbation velocity potential are expressed in terms of curvilinear coordinates which follow the body during its motion, thus allowing the boundary of the body to be considered as a fixed surface. Equations are simplified according to the slenderness of the body and the weakness of the non-uniformity of the unperturbed flow. These simplifications allow the pressure acting on the body to be determined analytically using the classical Bernoulli equation, which is then integrated over the body. The model is finally used to investigate the passive and the active swimming of a fish in a Karman vortex street.