On the spin-up and spin-down of a rotating fluid. Part 1. Extending the Wedemeyer model
On the spin-up and spin-down of a rotating fluid. Part 1. Extending the Wedemeyer model
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关于旋转流体的自旋向上和自旋向下。
DOI：
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发表时间：
1976
影响因子：
3.7
通讯作者：
P. Weidman
中科院分区：
文献类型：
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作者：
P. Weidman
将描述旋转圆柱体中流体自旋的韦德迈耶模型推广到包括自旋下降的情况。对于较小的Ekman数En，注意力集中在有限(恒定)加速度下的自旋加速和自旋减速。结果表明，当包含完全非线性的Ekman吸力时，传播波阵面附近的特征相交，从而导致无粘性模型的速度不连续。这种反常行为仅限于很小范围的Rossby数，并且不会出现在任何自旋减速解中。对于减速足够小的准定常流动，计算了圆柱壁上O(E_1/4Ω)剪切层中的瞬时自旋速度分布。给出了无限平行板之间脉冲自旋上、下的结果，并与Greenspan&Weinbaum和Benton给出的渐近解进行了比较。最后，计算了包含圆柱体和无限平行板几何结构的特征自旋加速和自旋减速时间。
The Wedemeyer model describing the spin-up of a fluid in a rotating cylinder is generalized to include the case of spin-down. Attention is focused on spin-up and spin-down at a finite (constant) acceleration for small Ekman numbers En. It is found that when the full nonlinear Ekman suction is included for spin-up from rest, the characteristics near the propagating wave front intersect, thus yielding an O(1) velocity discontinuity for the inviscid model. This anomalous behaviour is limited to only a small range of Rossby numbers and does not appear in any of the spin-down solutions. Transient spin-down velocity profiles in the O(E1/4Ω) shear layer at the cylindrical wall are calculated for the quasi-steady flow which occurs for sufficiently small decelerations. Results for impulsive spin-up and spin-down between infinite parallel plates are presented and compared with the asymptotic solutions given by Greenspan & Weinbaum and Benton. Finally, characteristic spin-up and spin-down times are computed for both the contained cylinder and the infinite-parallel-plates geometry.