NONLINEAR SATURATION OF ATMOSPHERIC GRAVITY-WAVES

The governing equation for atmospheric gravity waves is deduced; it contains nonlinear terms of up to third-order perturbations. This general equation is used to derive the nonlinear equation for the amplitude of the velocity perturbation in a quasi-monochromatic wave, taking into account the secular terms. It is shown that the amplitude of the vertical velocity perturbation which would exponentially grow with altitude in the linear approximation is restricted by a nonlinear stabilization, the maximum value being much smaller (by 1 or 2 orders of magnitude) than the sound velocity. The nonlinear evolution of the wave phase is also found. These results can be important for understanding interactions between the atmosphere and ionosphere.