要約

Nonlinear Kelvin−Helmholtz instability of two supersposed couple-stress fluids saturating a porous medium in the presence of normal electric fields when there are no surface charges at the interface is investigated in three dimensions via the viscous potential flow analysis. The multiple time scales method is used to obtain a dispersion relation for the linear problem and a Ginzburg−Landau equation with complex coefficients for the nonlinear problem, describing the behavior of the system. The stability conditions are obtained and discused both analytically and numerically in both linear and nonlinear cases in two- and three-dimensional disturbances. It is found, in the linear case, that the surface tension, porosity of the porous medium, kinematic viscosities, and kinematic viscoelasticities have stabilizing effects, while the fluid velocities and applied electric fields have destabilizing effects. In the nonlinear analysis, it is found that the medium permeability, porosity of porous medium, and surface tension have destabilizing effects, while the fluid velocities, electric fields, and kinematic viscoelasticities have stabilizing effects, and the kinematic viscosities have slightly stabilizing effects only after a critical wavenumber value. The stability of the system has been compared in two- and three-dimensional disturbances.