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The boundary conditions at the deformable interface between two contactingfluids are derived for the general case of the large-amplitude perturbations.The interface is modeled as perturbed free boundary that evolves in time, andthe non-linear description is performed and analyzed in a wide range ofphysical situations. The differential equations of the interfacial motion thusobtained may be useful in research of the non-linear development of theclassical hydrodynamic instabilities. They should play an important role in theunderstanding of the hydrodynamic phenomena associated with the flows involvingcomplex interfacial evolution including parametric control of the boundaries incontinua (for example, with electromagnetic field or/and vibration).

Derivation and analysis of the nonlinear boundary conditions at the deformable interface between two fluids