Laboratoire de Physique et Mécanique des Milieux Hétérogènes (PMMH UMR 7636) CNRS, ESPCI Paris, PSL Research University, Sorbonne Université, Université Paris Diderot, 10 rue Vauquelin, 75005 Paris, France
J R Soc Interface. 2018 Feb;15(139). doi: 10.1098/rsif.2017.0715.
Questions of energy dissipation or friction appear immediately when addressing the problem of a body moving in a fluid. For the most simple problems, involving a constant steady propulsive force on the body, a straightforward relation can be established balancing this driving force with a skin friction or form drag, depending on the Reynolds number and body geometry. This elementary relation closes the full dynamical problem and sets, for instance, average cruising velocity or energy cost. In the case of finite-sized and time-deformable bodies though, such as flapping flyers or undulatory swimmers, the comprehension of driving/dissipation interactions is not straightforward. The intrinsic unsteadiness of the flapping and deforming animal bodies complicates the usual application of classical fluid dynamic forces balance. One of the complications is because the shape of the body is indeed changing in time, accelerating and decelerating perpetually, but also because the role of drag (more specifically the role of the local drag) has two different facets, contributing at the same time to global dissipation and to driving forces. This causes situations where a strong drag is not necessarily equivalent to inefficient systems. A lot of living systems are precisely using strong sources of drag to optimize their performance. In addition to revisiting classical results under the light of recent research on these questions, we discuss in this review the crucial role of drag from another point of view that concerns the fluid-structure interaction problem of animal locomotion. We consider, in particular, the dynamic subtleties brought by the quadratic drag that resists transverse motions of a flexible body or appendage performing complex kinematics, such as the phase dynamics of a flexible flapping wing, the propagative nature of the bending wave in undulatory swimmers, or the surprising relevance of drag-based resistive thrust in inertial swimmers.
当涉及到物体在流体中运动的问题时,就会立即出现能量耗散或摩擦的问题。对于最基本的问题,即物体受到恒定的持续推进力,根据雷诺数和物体几何形状,可以建立一个直接的关系来平衡这个驱动力和表面摩擦或形状阻力。这个基本关系封闭了完整的动力学问题,并确定了例如平均巡航速度或能量成本。然而,对于有限大小和时间变形的物体,例如拍打飞行器或波动游泳者,驱动/耗散相互作用的理解并不简单。拍打和变形动物身体的固有非稳态使经典流体动力平衡的通常应用变得复杂。其中一个复杂性是因为物体的形状确实在随时间变化,不断加速和减速,而且因为阻力(更具体地说是局部阻力)的作用有两个不同的方面,同时对全局耗散和驱动力做出贡献。这导致了强阻力不一定等同于低效系统的情况。许多生命系统正是利用强阻力源来优化其性能。除了重新审视这些问题的最新研究对经典结果的影响外,我们还从与动物运动的流固相互作用问题有关的另一个角度讨论了阻力的关键作用。我们特别考虑了由二次阻力带来的动态细微差别,该阻力抵抗执行复杂运动的柔性体或附件的横向运动,例如柔性拍打翼的相位动力学、波动游泳者中的弯曲波的传播性质,或者基于阻力的惯性游泳者中阻力推力的惊人相关性。