The Two-Dimensional Steady Motion of a Viscous Fluid
The Two-Dimensional Steady Motion of a Viscous Fluid
复制标题
DOI：
10.1080/14786440408635327
复制
发表时间：
1915-04-01
影响因子：
1.6
通讯作者：
Jeffery, G. B.
中科院分区：
文献类型：
--
作者：
Jeffery, G. B.
假定运动是缓慢的，因而速度分量的平方和乘积可以忽略，这就取得了很大的成就。事实上，人们认为这是唯一有用的方法，因为运动方程本身就是在线性应力-应变关系的假设下形成的，而且这可能只有在运动足够慢的情况下才是合理的。另一方面，在流体的情况下，几乎没有证据表明线性定律失效，而且在任何情况下，只有通过研究不要求运动是流动的解，才有可能检验它的有效性。因此，获得一些不受这种限制的解是很重要的。在本文中，我们只注意平面运动.采用正交曲线坐标，并讨论了选择正交曲线坐标的可能性，使流线或常涡度线与一族坐标曲线相同。得到的最重要的解是对应于（1）圆弧形管道的运动，（2）旋转圆柱体之间的运动，表面上有给定的法向流，如离心泵，（3）两个以任意角度倾斜的无限平面之间的流动。
Much has been accomplished by assuming that the motion is slow, and that the squares and products of the velocity components may therefore be neglected. It has indeed been held that this is the only useful proceeding, since the equations of motion are themselves formed on the assmnption of a linear stress-strain relation, and this is probably only justifiable if the motion is sufficiently slow. On the other hand, there is very little evidence of the breakdown of the linear law in the case Of fluids, and in any case it is only possible to test its validity by an investigation of solutions which do not require the motion to be s] ow. It is, therefore, of some importance to obtain some solutions which are free from this limitation. In the present paper we confine our attention to plane motion. Orthogonal curvilinear coordinates are employed, and we discuss the possibility of so choosing them that either the stream-lines or the lines of constant vorticity are identical with one family of the coordinate curves. The most important solutions obtained are those which correspond to (1) the motion round a canal in the form of a circular arc,(2) the motion between rotating circular cylinders with a given normal flow over the surfaces, as ma centrifugal pump,(3) the flow between two infinite planes inclined at any angle.