Two-Dimensional Periodic Waves in an Inviscid Continuously Stratified Fluid

In this paper we study the propagation of two-dimensional periodic waves in an inviscid continuously stratified fluid with a free surface in the frequency range from 10^ - 4 to 5\,\, × \,\,10² Hz. Dispersion relations, as well as expressions for phase and group velocities for surface and internal waves in physically observable variables, are given. The fluid is shown to behave as homogeneous when the wavelength reaches values on the order of the stratification scale. As the wave frequency approaches the buoyancy frequency, the energy transfer rate decreases: the group velocity of surface waves tends to zero, while the phase velocity tends to infinity. In the case of infinitesimal perturbations of a stratified fluid with a free surface, surface and internal waves exist in separated frequency intervals.