A Nonlinear Azimuthal Instability of Hydromgantic Rigid-Rotating Column

This work examines a new approach to studying the nonlinear azimuthal instability analysis. The system consists of two rotating fluids through porous media in the influence of a uniform azi-muthal magnetic field. For gullibility, the problem is assumed in a planar configuration. The boundary-value problem reveals a differential equation of nonlinearity nature which controls the surface deflection of the interface. The investigation of this equation is based mainly on the homotopy perturbation technique. The linear and nonlinear stability criteria are conducted. Besides, the profile of the surface deflection is theoretically achievable. The numerical calcula-tions are done to display the effect of the several physical parameters on the stability profile. It is found that the ratio of the densities between the two fluid columns plays an interesting role in the stability picture in linear as well as the nonlinear approaches. For instance; a dual role of the density ratio occurs when the density of the inner column is greater than that of the outer one. Furthermore, the azimuthal wavenumber, like the axial wavenumber, plays a stabilizing influ-ence.