Azimuthal rotation in the axisymmetric meridional flow due to an electric-current source
Azimuthal rotation in the axisymmetric meridional flow due to an electric-current source
复制标题
电流源引起的轴对称子午流中的方位角旋转
DOI：
10.1017/s0022112083000245
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发表时间：
1983
影响因子：
3.7
通讯作者：
E. V. Shcherbinin
中科院分区：
文献类型：
--
作者：
V. Bojarevics;E. V. Shcherbinin
考虑了平面上电流点源的子午电磁力驱动的定常层流流动。以前对这个问题的研究(Shercliff 1970；Shilova&Shcherbinin 1971)导致了完整的Navier-Stokes方程的自相似解，类似于经典的Landau喷流。当超过临界电流值时，解决方案就会崩溃(Sozou 1971)。本文证明了当超过相应的临界雷诺数时，收敛的子午流对轴对称方位摄动是不稳定的。对于耦合的收敛和旋转流动，消除了流动解的破裂。物理过程是由排水涡的形成所暗示的。利用Gegenbauer函数展开，用Galerkin方法求解流体流动方程。研究了维持旋转的机制；流体区域中增加的角动量是通过向对称轴上游的粘性扩散和对流的平衡来维持的。考虑了涡旋形成的实验证据。
The steady laminar flow driven by the meridional electromagnetic force due to an electric-current point source on a plane is considered. The previous studies of the problem (Shercliff 1970; Shilova & Shcherbinin 1971) lead to a self-similar solution of the full Navier–Stokes equations analogous to the classic Landau jet. The solution breaks down when a critical electric-current magnitude is exceeded (Sozou 1971). In the present paper the converging meridional flow is shown to be unstable to an axisymmetric azimuthal perturbation when the corresponding critical Reynolds number is exceeded. The flow solution breakdown is eliminated for the coupled converging and rotating flow. The physical process is suggested by the draining-vortex formation. The fluid-flow equations are solved by the Galerkin method, using expansions in Gegenbauer functions. The mechanism sustaining the rotation is examined; the increased angular momentum in the fluid region is maintained by the balance of viscous diffusion upstream and convection to the axis of symmetry. The experimental evidence for vortex formation is considered.