Dynamics of the interface between immiscible liquids of different densities with low Froude number

Consideration is given to slow interfacial dynamics in a two-layer system of viscous fluids of comparable density. The fluid flow is governed by the two-dimensional Navier–Stokes equations where it is assumed that the inertial terms can be disregarded. A numerical methodology is presented which allows the study of the dynamics in the nonlinear regime. The numerical method is based on rewriting the interface conditions in terms of appropriate Green’s functions which are independent on the governing equations.