The current paper is concerned with the nonlinear stability analysis of rotating magnetic fluid columns. The rotation sources are a mixture of both uniform and oscillating behavior. The motivation behind tackling this topic is the increasing interest in atmospheric and oceanic motions. The system consists of two magnetic phase fluid that fills two infinite vertical cylinders. An azimuthal uniform magnetic field is penetrated on the system. The governing equations of motion, in terms of the Coriolis force and reduced pressure, along with Maxwell’s equation in the quasi-static approximations are considered. Consequently, the disturbance of the interface has an azimuthal behavior. The fluids are fully saturated in porous media. In light of the implication of the nonlinear boundary conditions, the solutions of the linearized equations of motion resulted in a nonlinear characteristic dispersion equation. Utilizing the homotopy perturbation technique, this equation is analyzed. A modification of the latter equation is made to seem like a nonlinear Klein–Gordon equation. The stability criteria are realized in linear as well as nonlinear approaches. A set of diagrams is graphed to illustrate the effects of several non-dimensional numbers on the stability profile in resonance as well as non-resonance cases.

本文涉及旋转磁流体柱的非线性稳定性分析。旋转源是均匀和振荡行为的混合。解决该主题的动机是人们对大气和海洋运动的兴趣日益增加。该系统由填充两个无限垂直圆柱体的两种磁相流体组成。方位均匀磁场穿透到系统上。考虑了在科里奥利力和减小的压力方面的运动控制方程，以及准静态近似中的麦克斯韦方程。因此，界面的干扰具有方位角行为。流体在多孔介质中完全饱和。考虑到非线性边界条件的影响，运动线性化方程的解产生了非线性特征色散方程。利用同伦摄动技术，对该方程进行了分析。对后一个方程的修改看起来像是非线性的Klein-Gordon方程。稳定性标准可通过线性和非线性方法来实现。绘制了一组图表，以说明共振和非共振情况下几个无量纲数字对稳定性分布的影响。