Detached shear layers in a rotating fluid
Detached shear layers in a rotating fluid
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DOI：
10.1017/s002211206700062x
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发表时间：
1967-07
影响因子：
3.7
通讯作者：
R. Hide;C. Titman
中科院分区：
文献类型：
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作者：
R. Hide;C. Titman
根据简单的理论论证，分离剪切层的出现通常应该表征快速旋转流体中的流体动力学运动。已经在非常简单的系统中产生和研究了这样的层，即，具有运动粘度V的均匀液体填充同轴地安装在围绕垂直轴以Ω0 rad/s旋转的转盘上的直立刚性圆柱形容器，并通过以Ω1 rad/S是一个半径为a cm、厚度为B cm的圆盘，它浸入液体中，其平面平行于容器的顶端壁和底端壁。通过改变Ω0、Ω1和a的Rossby数的范围，得到了ε <$（Ω1 + Ω0）/1/2（Ω1 + Ω0）的模从0·01到0·3，Ekman数E <$2v/a2（Ω1 + Ω0）从10−5到5 × 10−4。虽然该装置是轴对称的，但只有当|ε|没有超过某个临界值，|εT|是以关于旋转轴对称的相同性质为特征的流动。不然等|ε| > |εT|当ε为正值时，在垂直于旋转轴的平面内形成规则的波型，数量为M，当ε为负值时，形成钝椭圆。轴对称分离剪切层中的轴向流，以及当ε为正时表征非轴对称流的波型的均匀漂移率，以相对简单的方式依赖于ε和E。的依赖|εT|可以用经验关系式表示|εT| = AEn，其中A = 16·8 ± 2·2且n = 0·568 ± 0·013（=（4/7）×（1·000 −（0·005 ± 0·023））！），标准误差，25次测定。M对E的依赖性不强，但一般随ε的增加而减小。
The occurrence of detached shear layers should, according to straightforward theoretical arguments, often characterize hydrodynamical motions in a rapidly rotating fluid. Such layers have been produced and studied in a very simple system, namely a homogeneous liquid of kinematical viscosity v filling an upright, rigid, cylindrical container mounted coaxially on a turn-table rotating at Ω0 rad/s about a vertical axis, and stirred by rotating about the same axis at Ω1 rad/s a disk of radius a cm and thickness b’ cm immersed in the liquid with its plane faces parallel to the top and bottom end walls of the container. By varying Ω0, Ω1 and a, ranges of Rossby number, the modulus of ε ≡ (Ω1 + Ω0)/½ (Ω1 + Ω0), from 0·01 to 0·3, and Ekman number, E ≡ 2v/a2(Ω1 + Ω0), from 10−5 to 5 × 10−4 were attained. Although the apparatus was axisymmetric, only when |ε| did not exceed a certain critical value, |εT|, was the flow characterized by the same property of symmetry about the axis of rotation. Otherwise, when |ε| > |εT|, non-axisymmetric flow occurred, having the form in planes perpendicular to the axis of rotation of a regular pattern of waves, M in number, when ε was positive, and of a blunt ellipse when ε was negative. The axial flow in the axisymmetric detached shear layer, and the uniform rate of drift of the wave pattern characterizing the non-axisymmetric flow when ε is positive, depend in relatively simple ways on ε and E. The dependence of|εT| on E can be expressed by the empirical relationship |εT| = AEn, where A = 16·8 ± 2·2 and n = 0·568 ± 0·013 (= (4/7) × (1·000 − (0·005 ± 0·023))!), standard errors, 25 determinations. M does not depend strongly on E but generally decreases with increasing ε.