Abstract

Electrovortex flows are of great interest both from the viewpoints of theoretical magnetohydrodynamics and applications. They arise when the electric current of variable density passes through a conducting medium (such as a liquid metal). The interaction between the current and self magnetic field of the current induces a nonpotential electromagnetic force that causes a vortex flow of the liquid. As a model problem, we consider a stationary flow between two parallel planes. The flow is described by the stream function for which we obtain a nonlinear fourth-order partial differential equation. For moderate values of the electrovortex flow parameter, we investigate the problem by the asymptotic series expansion in the powers of this parameter. We describe the process of successive approximations of various degrees and present the flow pattern that is given by two first terms. This asymptotic solution is shown to be rather close to the numerical solution of the problem.

中文翻译：

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两平面之间慢轴对称电涡流方程解的渐近展开

摘要

从理论磁流体动力学和应用的观点来看，电涡流都引起了极大的兴趣。当可变密度的电流通过导电介质（例如液态金属）时，它们就会出现。电流与电流的自磁场之间的相互作用会引起非电位电磁力，从而导致液体涡流。作为模型问题，我们考虑两个平行平面之间的平稳流动。用流函数描述了流动，为此我们获得了一个非线性的四阶偏微分方程。对于中等大小的电涡流参数，我们通过渐近级数展开该参​​数的幂来研究该问题。我们描述了不同程度的逐次逼近过程，并给出了由两个第一项给出的流动模式。该渐近解被证明与问题的数值解非常接近。