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Communication Dans Un Congrès Année : 2013

Skin friction enhancement in a model problem of undulatory swimming

Résumé

To calculate the energy costs of swimming, it is crucial to evaluate the drag force originating from skin friction. In this paper we examine the assumption, known as the 'Bone-Lighthill boundary-layer thinning hypothesis', that undulatory swimming motions induce a drag increase because of the compression of the boundary layer. Studying analytically an incoming flow along a flat plate moving at a normal velocity as a limit case of a yawed cylinder in uniform flow under the laminar boundary layer assumption, we demonstrate that the longitudinal drag scales as the square root of the normal velocity component. This analytical prediction is interpreted in the light of a three-dimensional numerical simulation result for a plate of finite length and width. An analogous two-dimensional Navier-Stokes problem by artificially accelerating the flow in a channel of finite height is proposed and solved numerically, showing the robustness of the analytical results. Solving the problem for an undulatory plate motion similar to fish swimming, we find a drag enhancement which can be estimated to be of the order of 20 %.
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Dates et versions

hal-00919515 , version 1 (16-12-2013)

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Uwe Ehrenstein, Christophe Eloy. Skin friction enhancement in a model problem of undulatory swimming. 11th Internationl Conference on Numerical Analysis and Applied Mathematics (ICNAAM) 2013, Sep 2013, Rhodes, Greece. pp.273-276, ⟨10.1063/1.4825474⟩. ⟨hal-00919515⟩
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