Interfacial capillary waves in the presence of electric fields

Large amplitude capillary waves on an inviscid, incompressible fluid layer of density ρ1 bounded by a second inviscid, incompressible fluid of density ρ2 are computed in the presence of a uniform electric field acting in a direction parallel to the undisturbed configuration. Periodic travelling waves of arbitrary amplitudes and wavelengths are calculated and the effect of the electric field is studied. The solutions extend the results of Papageorgiou and Vanden-Broeck [D.T. Papageorgiou, J.-M. Vanden-Broeck, Large-amplitude capillary waves in electrified fluid sheets, J. Fluid Mech. 508 (2004) 71–88; D.T. Papageorgiou, J.-M. Vanden-Broeck, Antisymmetric capillary waves in electrified fluid sheets, Eur. J. Appl. Math. 16 (2004) 609–623] where the case of ρ2=0 was treated. Fully nonlinear solutions are computed using boundary integral equation methods. It is shown that there are both symmetric and antisymmetric waves and their characteristics are explored and compared. When there is a jump in the undisturbed horizontal velocities, the flow is susceptible to Kelvin–Helmholtz instability. It is shown analytically in the linear regime, that even in the absence of surface tension, the flow is stabilized by sufficiently large electric fields. In such situations two wave speeds are possible for given electric fields and we construct these branches numerically when the amplitudes are not infinitesimal, both in the absence and presence of surface tension.