Stability of a viscous liquid contained between two rotating cylinders
Stability of a viscous liquid contained between two rotating cylinders
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DOI：
10.1098/rsta.1923.0008
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发表时间：
1923-01-01
影响因子：
--
通讯作者：
Taylor, GI
中科院分区：
文献类型：
--
作者：
Taylor, GI
近年来，有关流体流过固体边界的信息积累了很多。到目前为止进行的所有实验似乎都表明，在所有情况下，如果运动足够慢，稳定运动是可能的，但如果流体的速度超过一定的极限，取决于流体的粘度和边界的形状，稳定运动就会破裂，涡流就会出现。为了发现流体不稳定性的某种数学表示，人们做了很多尝试，但到目前为止，他们在每一种情况下都没有成功。例如，开尔文、瑞利、索默菲尔德、奥尔、米塞斯、霍普和其他人已经讨论过流体被包含在两个以均匀相对速度运动的无限平行平面之间的情况。它们都可以得出结论：该系统的基本小扰动是稳定的。虽然用无限大的平面进行实验肯定是不可能的，但人们普遍认为，如果两个平面的相对速度足够大，这种情况下的运动将是湍流的。
In recent years much information has been accumulated about the flow of fluids past solid boundaries. All experiments so far carried out seem to indicate that in all cases steady motion is possible if the motion be sufficiently slow, but that if the velocity of the fluid exceeds a certain limit, depending on the viscosity of the fluid and the configuration of the boundaries, the steady motion breaks down and eddying flow sets in. A great many attempts have been made to discover some mathematical representation of fluid instability, but so far they have been unsuccessful in every case. The case, for instance, in which the fluid is contained between two infinite parallel planes which move with a uniform relative velocity has been discussed by Kelvin, Rayleigh, Sommerfeld, Orr, Mises, Hope, and others. Each of them cam e to the conclusion that the fundamental small disturbances of this system are stable. Though it is necessarily impossible to carry out experiments with infinite planes, it is generally believed that the motion in this case would be turbulent, provided the relative velocity of the two planes were sufficiently great.