THE NONLINEAR INTERNAL GRAVITY WAVES IN STRATIFIED FLUID

In this paper, starting from the equations of the nonlinear internal gravity waves in stratified fluid, using the method of the Taylor expansion nearby the equilibrium point for the nonlinear terms, we find the analytical solutions for nonlinear internal gravity waves. The linear internal gravity waves and solitary waves are its special cases. The nonlinear internal gravity waves satisfy the well-known KdV (Karteweg-de Vries) equation. The nonlinear internal gravity waves are different from linear waves in character. The former dispersive relation contains the amplitude, but the latter does not. The larger the amplitude and the wavelength the faster are waves for the nonlinear internal gravity waves. The smaller the stability of the stratification, the larger is the wavelength (or the width). Some phenomena such as squall line, cumulus, turbulent mass structure in atmosphere, and thermocline in ocean have these natures.