Abstract
The analytical methods by which nonlinear interfacial fluid motions can be modelled are introduced. The partial differential equations which completely satisfy the interfacial conditions or the free surface conditions are derived. In particular, the model equation of internal waves involves two indefinite functions and these are related to the difference of velocities and the difference of pressure gradients at the interface respectively.
Furthermore, for irrotational motions the indefinite function can be determined so as to satisfy other boundary conditions such as bottom conditions. Finally, the modelling of the Rayleigh-Taylor problem and the breaking waves in the finite depth channel are discussed by the present method.
