Transition from ciliary to flapping mode in a swimming mollusc : flapping flight as a bifurcation in Re ω
Transition from ciliary to flapping mode in a swimming mollusc : flapping flight as a bifurcation in Re ω
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发表时间：
2002
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通讯作者：
By Stephen Childress;R. Dudley
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作者：
By Stephen Childress;R. Dudley
从观察游泳的无壳的翼足类软体动物Clione anarctica，我们比较游泳速度的生物体单独使用纤毛表面的速度实现由同一生物体使用一对扑翼。在5-20的范围内的游泳雷诺数Re以上，扑动占主导地位的运动。我们测试的假设，Re 0.5 -20标志着这些生物的“扑翼飞行”的开始。我们考虑这样一个命题，即对于运动完全由体长L和低于雷诺数Reω = ωL /ν的某个有限临界值的频率ω决定的生物体来说，向前的往复扑翼飞行是不可能的。对于一个自相似的物体形状族，临界雷诺数应该只取决于物体的几何形状和用于旋转的循环运动。我们给出了这样一个临界雷诺数在我们的数据的证据，并研究了在几个简化的理论模型的分歧。我们进一步认为，这种分歧标志着离开自然运动的低雷诺数或斯托克斯境界，并进入高雷诺数或欧拉境界。这是因为在不稳定时获得的平衡游泳或飞行速度Uf是由粘性流体的力学决定的，其值Ref = Uf L/v不小。
From observations of swimming of the shell-less pteropod mollusc Clione antarctica we compare swimming velocities achieved by the organism using ciliated surfaces alone with velocities achieved by the same organism using a pair of flapping wings. Flapping dominates locomotion above a swimming Reynolds number Re in the range 5–20. We test the hypothesis that Re ≈ 5–20 marks the onset of ‘flapping flight’ in these organisms. We consider the proposition that forward, reciprocal flapping flight is impossible for locomoting organisms whose motion is fully determined by a body length L and a frequency ω below some finite critical value of the Reynolds number Reω = ωL /ν. For a self-similar family of body shapes, the critical Reynolds number should depend only upon the geometry of the body and the cyclic movement used to locomote. We give evidence of such a critical Reynolds number in our data, and study the bifurcation in several simplified theoretical models. We argue further that this bifurcation marks the departure of natural locomotion from the low Reynolds number or Stokesian realm and its entry into the high Reynolds number or Eulerian realm. This occurs because the equilibrium swimming or flying speed Uf obtained at the instability is determined by the mechanics of a viscous fluid at a value of Ref = Uf L/ν that is not small.