This paper investigates the nonlinear instability of a non-Newtonian fluid of the Walters’ B type. The fluids fill the regions inside and outside a vertical circular cylinder. An axial electric field of uniform strength is pervaded along the axis of the jet. The fluids are saturated in porous media. Typically, the nonlinear analysis is based on solving the linear governing equations of motion, then applying the convenient nonlinear boundary conditions. This methodology yields a nonlinear characteristic equation which governs the behavior of the interface deflection. As the nonlinear terms are omitted, a linear dispersion relation arises. Therefore, the stability criteria are analytically analyzed and numerically confirmed. The nonlinear approach depends on the multiple time scale technique together with the support of the Taylor theory. This approach resulted in a Ginzburg–Landau equation. Consequently, the stability criteria are achieved in both analytical and numerical analysis. Furthermore, by means of the expanded frequency analysis, a bounded approximate solution of the amplitude of the surface waves is accomplished. The homotopy perturbation method (MPM) is utilized to obtain an approximate distribution of the conducted artificial frequency. Additionally, the generating function of the interface is graphically represented. Several special cases are reported upon convenient data choices. Regions of stability and instability are addressed. In the stability profile, the electric field intensity is plotted versus the wave number. The influences of the parameters on the stability are identified. The nonlinear stability approach divides the phase plane into several parts of stability/instability.

本文研究了沃尔特斯B型非牛顿流体的非线性不稳定性。流体填充垂直圆柱体内部和外部的区域。均匀强度的轴向电场沿射流的轴线渗透。流体在多孔介质中饱和。通常，非线性分析是基于求解运动的线性控制方程式，然后应用方便的非线性边界条件。这种方法产生了一个非线性特征方程，该方程控制着界面偏转的行为。由于省略了非线性项，所以产生了线性色散关系。因此，对稳定性标准进行了分析和数值确认。非线性方法取决于多时标技术以及泰勒理论的支持。这种方法产生了Ginzburg-Landau方程。因此，在分析和数值分析中都达到了稳定性标准。此外，借助于扩展的频率分析，获得了表面波振幅的有界近似解。同伦摄动法（MPM）用于获得传导人工频率的近似分布。另外，以图形方式表示界面的生成功能。根据方便的数据选择，报告了几种特殊情况。解决了稳定和不稳定的区域。在稳定性曲线中，绘制了电场强度与波数的关系图。确定了参数对稳定性的影响。