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Note on the swimming of an elongated body in a non-uniform flow

Published online by Cambridge University Press:  28 January 2013

Fabien Candelier ,
Mathieu Porez  and
Frederic Boyer
Fabien Candelier*
Affiliation:
Aix-Marseille Université – IUSTI (UMR CNRS 7343), 60 rue Joliot-Curie, 13 453 Marseille CEDEX 13, France
Mathieu Porez
Affiliation:
Ecole des Mines de Nantes – IRCCyN (UMR CNRS 6597), La Chantrerie, 4 rue Alfred Kastler, BP 2072, 44 307 Nantes, France
Frederic Boyer
Affiliation:
Ecole des Mines de Nantes – IRCCyN (UMR CNRS 6597), La Chantrerie, 4 rue Alfred Kastler, BP 2072, 44 307 Nantes, France
*
†Email address for correspondence: [email protected]
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Abstract

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 Kármán vortex street.

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics Biological Fluid Dynamics: Swimming/flying
Type
Papers
Information
Journal of Fluid Mechanics , Volume 716 , 10 February 2013 , pp. 616 - 637
Copyright
©2013 Cambridge University Press

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Candelier et al. supplementary movie

Passive swimming of a body in a vortex street. V_10 is the head velocity and Vf_10 is the unperturbed fluid velocity at the middle of the rows, along the axial direction. Distance between two consecutive vortices on the same row: 0.208 m. Distance between the two rows: 0.07 m. Length of the body: 0.178 m.

Download Candelier et al. supplementary movie(Video)
Video 8.7 MB