Linear Surface and Internal Gravity Waves: Problems Formulation, Main Approximations of Dispersion Relations

This paper considers formulations of problems describing the dynamics of linear surface gravity waves. The analytical properties of the dispersion relations describing surface and internal gravity waves for various regimes of wave generation are discussed. It is shown that, in the Boussinesq approximation, linear internal and surface gravity waves are completely decoupled and can be treated independently of each other. In particular, replacing the boundary conditions at the free surface of a stratified medium with the “rigid-lid” approximation does not change the fundamental dispersion relations that describe the dynamics of linear internal gravity waves in this medium.