Non-linear temporal dynamics of two-mode interactions of magnetized flow

摘要: Abstract This paper considers, in the frame work of model two superposed layers viscous-potential incompressible magnetic fluids, problem on formation resonant waves modes interface between fluids that arisen as a result second-harmonic resonance. The moving with uniform velocities parallel to their are stressed by tangential field. analysis includes linear, well non-linear effects where analytical solutions constructed using method multiple scales, both space and time, hence solvability conditions correspond (convergent) obtained. then exploited derive more general system partial differential equations complex coefficients governing amplitudes waves. These examined for corresponding sinusoidal wavetrains consequently different kinds instabilities demonstrated. stability criterion each case is derived discussed analytically graphically.