Comprehensive linear stability study of flow in an annular layer of electrolyte driven by the action of the Lorentz force is conducted following the analysis of steady axisymmetric solutions of Suslov et al. (J. Fluid Mech., vol. 828, 2017, pp. 573–600). It is shown that an experimentally observed instability in the form of anticyclonic moving vortices reported in Perez-Barrera et al. (Magnetohydrodynamics, vol. 51 (2), 2015, pp. 203–213) develops on a background of the basic flow consisting of two tori with the opposite azimuthal vorticity components. It is found that, while the background flow is driven electromagnetically, the appearance of vortices is purely due to hydrodynamic effects: shear of the flow and centrifugal inertial forcing. The current study has also revealed that the unstable two-torus basic flow has a stable single-torus counterpart, both emanating from a saddle-node bifurcation of steady states when the Lorentz force is sufficiently strong. The transition from a one-torus to two-torus flow at weaker forcing is abrupt and leads to the appearance of vortices as soon as it occurs. The ranges of layer depths and Reynolds numbers for which vortices develop on a steady background are determined. Subsequently, weakly nonlinear amplitude expansion is used to find an approximate unsteady solution beyond the saddle-node bifurcation.

中文翻译：

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环形层中电磁驱动电解质流的线性稳定性和鞍节点分叉

在对 Suslov 等人的稳态轴对称解的分析之后，对由洛伦兹力驱动的环形电解质层中的流动进行了全面的线性稳定性研究。（J. Fluid Mech.，第 828 卷，2017 年，第 573-600 页）。结果表明，Perez-Barrera 等人报道的反气旋运动涡旋形式的实验观察到的不稳定性。(Magnetohydrodynamics, vol. 51 (2), 2015, pp. 203–213) 在基本流动的背景下发展，该流动由两个具有相反方位角涡度分量的环面组成。发现，虽然背景流是由电磁驱动的，但涡流的出现纯粹是由于流体动力学效应：流的剪切力和离心惯性力。目前的研究还表明，当洛伦兹力足够强时，不稳定的双圆环基本流具有稳定的单圆环对应物，两者都源自稳态的鞍节点分叉。在较弱的强迫下从一个圆环流到两个圆环流的过渡是突然的，并且一旦发生就会导致涡流的出现。确定在稳定背景上形成涡流的层深度和雷诺数的范围。随后，弱非线性振幅扩展被用于寻找超出鞍节点分岔的近似非定常解。在较弱的强迫下从一个圆环流到两个圆环流的过渡是突然的，并且一旦发生就会导致涡流的出现。确定在稳定背景上形成涡流的层深度和雷诺数的范围。随后，弱非线性振幅扩展被用于寻找超出鞍节点分岔的近似非定常解。在较弱的强迫下从一个圆环流到两个圆环流的过渡是突然的，并且一旦发生就会导致涡流的出现。确定在稳定背景上形成涡流的层深度和雷诺数的范围。随后，弱非线性振幅扩展被用于寻找超出鞍节点分岔的近似非定常解。