Surface and internal waves in a stratified layer of liquid and an analysis of the impedance boundary conditions

The surface and internal waves in a multilayered ideal liquid for specified displacements of the bottom are considered. The upper surface of the liquid is either free or displacements are specified on it. In the long-wave approximation, asymptotically accurate models of the waves propagating along the surface layers of an incompressible liquid are constructed both for intense stratification (the ratio of the densities of neighbouring layers are associated with a small parameter) and for weak stratification. The important case of this problem of the dynamic contact of rigid bodies through a layer of incompressible or compressible liquid is investigated. High-order impedance boundary conditions are constructed and the results of testing them using the exact solutions are presented.