Nonlinear Kelvin–Helmholtz instability of magnetized surface waves on a subsonic gas–viscous potential liquid interface

A nonlinear stability analysis, of magnetic fluids, was carried out for interfacial waves between a subsonic inviscid gas and viscous streaming liquid when a normal constant magnetic field is present. The viscosity term in the problem was carried out using the viscous potential theory. The nonlinear analysis results nonlinear partial differential equations, for different cases, using multiple scales method. Using the modulation concept, we have discussed different numerical examples to show the effects of the system parameters on criteria of the interfacial waves (in)stability.