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Three-dimensional extension of Lighthill's large-amplitude elongated-body theory of fish locomotion

Published online by Cambridge University Press:  11 March 2011

FABIEN CANDELIER ,
FREDERIC BOYER  and
ALBAN LEROYER
FABIEN CANDELIER*
Affiliation:
Université Aix-Marseille 2, IUSTI, Technopôle de Château Gombert, 60 rue Joliot-Curie, 13453 Marseille CEDEX 13, France
FREDERIC BOYER
Affiliation:
Ecole des Mines de Nantes, La Chantrerie, 4 rue Alfred Kastler, BP 20722, 44307 Nantes, France
ALBAN LEROYER
Affiliation:
Laboratoire de Mécanique des Fluides, Ecole Centrale Nantes, 1 rue de la Noë, BP 92101, 44321 Nantes CEDEX 3, France
*
†Email address for correspondence: fabien.candelier@univmed.fr
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Abstract

The goal of this paper is to derive expressions for the pressure forces and moments acting on an elongated body swimming in a quiescent fluid. The body is modelled as an inextensible and unshearable (Kirchhoff) beam, whose cross-sections are elliptic, undergoing prescribed deformations, consisting of yaw and pitch bending. The surrounding fluid is assumed to be inviscid, and irrotational everywhere, except in a thin vortical wake. The Laplace equation and the corresponding Neumann boundary conditions are first written in terms of the body coordinates of a beam treating the body as a fixed surface. They are then simplified according to the slenderness of the body and its kinematics. Because the equations are linear, the velocity potential is sought as a sum of two terms which are linked respectively to the axial movements of the beam and to its lateral movements. The lateral component of the velocity potential is decomposed further into two sub-components, in order to exhibit explicitly the role of the two-dimensional potential flow produced by the lateral motion of the cross-section, and the role played by the curvature effects of the beam on the cross-sectional flow. The pressure, which is given by Bernoulli's equation, is integrated along the body surface, and the expressions for the resultant and the moment are derived analytically. Thereafter, the validity of the force and moment obtained analytically is checked by comparisons with Navier–Stokes simulations (using Reynolds-averaged Navier–Stokes equations), and relatively good agreements are observed.

JFM classification

Biological Fluid Dynamics: Swimming/flying
Type
Papers
Information
Journal of Fluid Mechanics , Volume 674 , 10 May 2011 , pp. 196 - 226
Copyright
Copyright © Cambridge University Press 2011

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