Insightful inspection of the nonlinear instability of an azimuthal disturbance separating two rotating magnetic liquid columns

Abstract The nonlinear stability examination of two revolving magnetized liquid columns connecting two completely submerged fluids in a permeable region is the aim of the existing paper. Two endless vertical cylinders occupied with two magnetic fluids make up the present structure. Significantly, the disturbance at the border displays an azimuthal behavior. The entire structure is activated by an azimuthal unchanging magnetic field (MF). The increasing interest in the atmospheric and oceanic dynamics is the primary motivation in exploring this problem. To relax the complication of the mathematical processes, the viscous potential theory (VPT) is established. The motion is assessed using three basic coexistent field formulations: Maxwell's formula, Brinkman's formula, and the continuity condition, in the construction of the Coriolis force and centrifugal implications. The explanations of the linearized formula of motion produce a nonlinear categorizing diffusion structure because of the implications of the nonlinear boundary conditions (BCs). The non-perturbative approach (NPA) based on the He's frequency formulation (HFF) is employed to transform the nonlinear characteristic ordinary differential equation (ODE) into a linear one. A short description of the NPA is also presented. The nonlinear ODE with real and imaginary coefficients is exposed by the stability analysis. The stability requirements are implemented using only a nonlinear analysis. As demonstrated, as an unusual state, it is exposed that ignoring the Weber number removes all complex items of the nonlinear formulation. Physically, this means the absence of the angular velocities from the physical model. For both the real and complex situations of the original equation, the stability remains unchanged. It is found that the azimuthal MF, rotating parameter, and Darcy’s numeral have a maintenance impact. On the other hand, the azimuthal wave numeral has a destabilizing one. Several polar designs are drawn to agreement the stability situations.