Nonlinear instability of surface waves between viscous–liquid and subsonic‐gas layers subject to uniform oblique magnetic field

Abstract

AbstractNonlinear instability of surface waves between viscous–liquid and inviscid‐gas layers is discussed. The two fluids are magnetic and subjected to uniform oblique magnetic field. The gas is subsonic and the viscosity is introduced by viscous potential approximation. The evolution equations near and on the marginal state are derived by means of multiple scales technique. The stability criteria of the waves are obtained by the modulation idea. Many special cases of dispersion equation as well as solvability conditions correspond well the similar ones in the literature. Various numerical applications have been investigated to reveal the parameters effects on the system stability. Linear results show dual influences for magnetic field, sum of inclination angles and permeability ratio whereas the wavelength, gas motion, and inclination angle in the liquid tend to destabilize the flow. Nonlinear applications reveal dual role for the gas thickness, while it has a linear stable‐role. Moreover, nonlinearity shows dual roles for viscosity and liquid thickness, which have no influences according to linear theory. The investigation of stability using nonlinear theory seems more accurate to describe the (un)stable influences comparing with the linear one. The current work may be useful to give more accurate comprehension of stability process as well as to obtain the required conditions of stability by designing suitable devices, which control the model parameters.