Estimate of the applicability limits of a linear theory of internal waves

Using a perturbation method, the applicability limits of a linear theory of internal gravity waves are estimated. It is shown that over a wide range of wavelengths, typical of a real ocean, in studying the dynamics of internal gravity waves it is possible to use a linear approximation, which confirms the validity and adequacy of this approximation for the corresponding spatial and temporal scales of the linear model of wave dynamics.