Variational properties of steady fall in Stokes flow
Variational properties of steady fall in Stokes flow
复制标题
斯托克斯流稳态下降的变分特性
DOI：
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发表时间：
1972
影响因子：
3.7
通讯作者：
H. Weinberger
中科院分区：
文献类型：
--
作者：
H. Weinberger
它示出，对于一个给定的身体和一个给定的取向g总是有一个位置的质心，产生一个稳定的下降运动在一个非常粘性的流体与g垂直，并在一般情况下，与旋转的垂直轴。相应的终端稳定速度是有界的几个变分原理。推导了不同下落方向的福尔斯的终端速度之间的关系以及终端速度与物体几何形状之间的关系。特别地，证明了对于一大类细长体，由Burgers（1938）的细长体理论得到的阻力的第一近似是正确的。因此，长轴垂直和水平的福尔斯的终端速度之比接近2。
It is shown that for a given body and a given orientation g there is always a position of the centre of mass which produces a stable falling motion in a very viscous fluid with g vertical and, in general, with a spin about the vertical axis. The corresponding terminal settling speed is bounded by means of several variational principles. Relations between the terminal speeds for falls with different downward directions and between the terminal speed and the geometry of the body are deduced. In particular, it is proved that for a large class of slender bodies the first approximation to the drag obtained from the slender-body theory of Burgers (1938) is correct. It follows that the ratio of the terminal speeds for falls with the long axis vertical and horizontal is near two.