On the Self-Displacement of Deformable Bodies in a Potential Fluid Flow

Munnier, Alexandre

doi:10.1142/s021820250800325x

Cited by 15 publications

(32 citation statements)

References 29 publications

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“…Further, we show that the solution is analytic and can be continued indefinitely unless a collision between two bodies or between a body with a fixed boundary of the fluid domain occurs. Such result has already be obtained in a more general case in [26] but the proof we give here has been significantly simplified.…”

supporting

confidence: 54%

“…It is a non-trivial result of shape sensitivity analysis which has already been proved in [26]. It entails that all of the terms in (3.3) are analytic with respect to q and also with respect toq for they are linear or quadratic with respect to this second variable.…”

Section: Well-posedness Of the Euler-lagrange Equationsmentioning

confidence: 94%

“…The proof is given in [26] in a more general framework. Assuming additional regularity on ∂F 0 , we can compute the partial derivatives of J ij : Proposition B.2 Assume that F 0 is of class C 1,1 and that the mapping s → φ s ∈ D m is of class C 2 with m ≥ 2.…”

Section: B Shape Sensitivity Analysismentioning

confidence: 99%

“…Nevertheless, among numerous mathematical articles studying fish locomotion, most of them address the case of a potential flow which is by definition vortex-free like in the works of Kelly and Murray [14], Kozlov and Onishchenko [15], Kanso, Marsden, Rowley and Melli-Huber [13], Melli, Rowley and Rufat [22] and Munnier [26]. It is also the point of view we have chosen in what follows and on which we focus from now on.…”

mentioning

confidence: 99%

“…Articulated bodies are composed of rigid solids linked together by means of holonomic constraints and can be seen as a particular case of the more general concept of shape-changing bodies as it has been described in [26]. The holonomic constraints govern the relative position of the rigid parts composing the articulated bodies.…”

mentioning

confidence: 99%

See 4 more Smart Citations

Locomotion of Articulated Bodies in an Ideal Fluid: 2d Model With Buoyancy, Circulation and Collisions

Munnier

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2010

Math. Models Methods Appl. Sci.

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Articulated solid bodies are shape-changing bodies made of rigid solids linked together by means of holonomic constraints prescribed as functions of time. In this paper we study the locomotion of such swimming devices in an ideal fluid. Our study ranges over a wide class of problems: any number of immersed bodies are involved (without being hydrodynamically decoupled), the system fluid-bodies can be partially of totally confined and circulation, buoyancy and collisions between bodies are taken into account. We determine the Euler-Lagrange equation governing the dynamic of the system, study its well-posedness and describe a numerical scheme used in a Matlab toolbox (Biohydrodynamics Toolbox) that has been designed to realize easily related numerical simulations.

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supporting

confidence: 54%

Section: Well-posedness Of the Euler-lagrange Equationsmentioning

confidence: 94%

Section: B Shape Sensitivity Analysismentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Locomotion of Articulated Bodies in an Ideal Fluid: 2d Model With Buoyancy, Circulation and Collisions

Munnier

Pinçon

2010

Math. Models Methods Appl. Sci.

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Point vortex dynamics as zero-radius limit of the motion of a rigid body in an irrotational fluid

2018

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The point vortex system is usually considered as an idealized model where the vorticity of an ideal incompressible two-dimensional fluid is concentrated in a finite number of moving points. In the case of a single vortex in an otherwise irrotational ideal fluid occupying a bounded and simply-connected two-dimensional domain the motion is given by the so-called Kirchhoff-Routh velocity which depends only on the domain. The main result of this paper establishes that this dynamics can also be obtained as the limit of the motion of a rigid body immersed in such a fluid when the body shrinks to a massless point particle with fixed circulation. The rigid body is assumed to be only accelerated by the force exerted by the fluid pressure on its boundary, the fluid velocity and pressure being given by the incompressible Euler equations, with zero vorticity. The circulation of the fluid velocity around the particle is conserved as time proceeds according to Kelvin's theorem and gives the strength of the limit point vortex. We also prove that in the different regime where the body shrinks with a fixed mass the limit dynamics is governed by a second-order differential equation involving a Kutta-Joukowski-type lift force.To prove these results, in a first step we reformulate the dynamics of the body in order to make more explicit different kind of interactions with the fluid. Precisely we establish that the Newton-Euler equations of translational and rotational dynamics of the body can be seen as a 3-dimensional ODE with

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Locomotion of Deformable Bodies in an Ideal Fluid: Newtonian versus Lagrangian Formalisms

Munnier

2009

J Nonlinear Sci

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This paper is concerned with comparing Newtonian and Lagrangian methods in Mechanics for determining the governing equations of motion (usually called Euler-Lagrange equations) for a collection of deformable bodies immersed in an incompressible, inviscid fluid whose flow is irrotational. The bodies can modify their shapes under the action of inner forces and torques and are endowed with thrusters, what means that they can generate fluid jets by sucking and blowing out fluid through some localized parts of their boundaries. These capabilities may allow them to propel and steer themselves. Our first contribution is to prove that under smoothness assumptions on the fluid-bodies interface, Newtonian and Lagrangian formalisms yield the same equations of motion. However and rather surprisingly this is no longer true for nonsmooth shaped bodies. The second novelty brought in in this paper is to treat for the first time a broad spectrum of problems in which several bodies undergoing any kind of deformation can be involved and to display the Euler-Lagrange equations under a form convenient to study locomotion and to perform numerical simulations. These equations have been used to develop a Matlab toolbox (Biohydrodynamics Toolbox) that allows to study animal locomotion in a fluid or merely the motion of submerged rigid solids. Examples of such simulations are given in this paper.

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On the Self-Displacement of Deformable Bodies in a Potential Fluid Flow

Cited by 15 publications

References 29 publications

Locomotion of Articulated Bodies in an Ideal Fluid: 2d Model With Buoyancy, Circulation and Collisions

Locomotion of Articulated Bodies in an Ideal Fluid: 2d Model With Buoyancy, Circulation and Collisions

Point vortex dynamics as zero-radius limit of the motion of a rigid body in an irrotational fluid

Locomotion of Deformable Bodies in an Ideal Fluid: Newtonian versus Lagrangian Formalisms

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