Axisymmetric flow in a cylindrical tank over a rotating bottom. Part I. Analysis of boundary layers and vertical circulation
Axisymmetric flow in a cylindrical tank over a rotating bottom. Part I. Analysis of boundary layers and vertical circulation
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旋转底部上方的圆柱形罐中的轴对称流动。
DOI：
10.1088/1873-7005/aa8bef
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发表时间：
2017
影响因子：
1.5
通讯作者：
Iga Keita
中科院分区：
文献类型：
--
作者：
Matsunobu;T.;and H. L. Tanaka;水田元太;Takumi Matsunobu and Hiroshi L. Tanaka;Iga Keita
本文研究了旋转底部圆柱形贮箱内的轴对称流动，得到了近似解和解析表达式。内部区域包括大部分流体，由两个子区域组成。结果表明，在内部区域形成与底部转速相同的刚体旋转流，在外部内部子区域形成具有恒定角动量的势流。然而，划分这两个子区域的半径尚未确定。为了确定这个半径，边界层的结构进行了详细的研究。这些边界层围绕内部区域，并且包括内部区域与罐的侧壁之间、内部与底部之间以及内部内部子区域与外部内部子区域之间的边界。通过连接边界层中的流动，建立了作为一个整体的垂直环流，从而成功地确定了划分两个内部子区域的半径，作为水层区域纵横比的函数。这种轴对称流将被用来作为基本状态，从理论上研究在实验室实验中观察到的各种非轴对称现象。
Axisymmetric flow in a cylindrical tank over a rotating bottom is investigated and its approximate solution with an analytic expression is obtained. The interior region, comprising the majority of the fluid, consists of two sub-regions. It is easily shown that a rigid-body rotational flow with the same rotation rate as that of the bottom is formed in the inner interior and that a potential flow with constant angular momentum occurs in the outer interior sub-region. However, the radius that divides these two sub-regions has not been determined. To determine this radius, the structures of the boundary layers are investigated in detail. These boundary layers surround the interior regions, and include the boundaries between the interior region and the side wall of the tank, between the interior and the bottom, and between the inner and outer interior sub-regions. By connecting the flows in the boundary layers, the vertical circulation as a whole is established, and consequently the radius dividing the two interior sub-regions is successfully determined as a function of the aspect ratio of the water layer region. This axisymmetric flow will be utilized as the basic state for investigating theoretically various non-axisymmetric phenomena observed in laboratory experiments.