Optimal swimming of flagellated micro-organisms
Optimal swimming of flagellated micro-organisms
复制标题
带鞭毛微生物的最佳游动
作者：
O. Pironneau;D. Katz
本文研究了鞭毛的波动，推动一个微生物在一个给定的速度，同时最大限度地减少其消耗的流体动力学能量。这项研究分为两个基本部分。第一部分是一个定性调查的一般性质的波动，是流体动力学最佳的瞬时意义上。结果表明，一个明显的滑动的整个鞭毛沿着其瞬时轴是根本的，这样的运动，虽然一个额外的变形是必要的，以补偿存在的有机体的头部。周期性或半周期性的波动被清楚地提出，并且必须由在与推进相反的方向上传播的行波组成。本文的第二部分是一个定量查询的参数值，优化给定的周期波形的时间平均意义上。波的振幅和波长的数量之间的权衡是特别感兴趣的。得到了小振幅正弦波和有限振幅正弦波的结果。对于后者，振幅约为波长六分之一的单个波长是最佳的。研究了头部抽搐运动的意义。结果是一致的定性研究，并强调需要抑制这种运动。的影响，连续力系数的依赖波形被认为是旋转俯仰运动的物理意义进行评估。
This paper studies flagellar undulations that propel a micro-organism at a given speed while minimizing its expenditure of hydrodynamical energy. The study is in two basic parts. The first part is a qualitative inquiry into the general nature of undulations that are hydrodynamically optimal in the instantaneous sense. The results indicate that an apparent sliding of the entire flagellum along its instantaneous axis is fundamental to such motions, although an additional deformation is necessary to compensate for the presence of the organism's head. Periodic or semi-periodic undulations are clearly suggested, and must consist of travelling waves propagated in the direction opposite to propulsion. The second part of the paper is a quantitative inquiry as to the values of parameters that optimize given periodic wave shapes in the time-average sense. The trade-off between wave amplitude and the number of wavelengths is of particular interest. Results are obtained for small amplitude sinusoidal waves and finite amplitude sawtooth waves. For the latter, a single wavelength with amplitude roughly one-sixth of the wavelength is optimal. The significance of the twitching movements of the head is investigated. The results are consistent with the qualitative study and emphasize the need to inhibit such motions. The implications of the dependence of resistive-force coefficients upon wave shape are considered, and the physical significance of rotational pitching motions is assessed.