Nonlinear Internal Gravity Waves and Their Interaction with the Mean Wind

Abstract

The interaction of a, wave packet of internal gravity waves with the mean wind is investigated, for the when there is a region of wind shear and also a critical level. The principal equations are the Doppler-shifted dispersion relation, the equation for conservation of wave action, and the mean momentum equation in which the mean wind is accelerated by a ?radiation stress? tensor due to the waves. These equations are integrated numerically to study the behavior of a wave packet approaching a critical level, where the horizontal phase speed matches the mean wind. The results demonstrate the exchange of energy from the waves to the mean wind in the vicinity of the critical level, as a function of the initial wave amplitude and the dissipation. For small initial wave amplitudes (so small that changes in the mean wind do not affect the wave packet), the wave packet narrows and grows in magnitude as it propagates toward the critical level, until it reaches a maximum, after which it is strongly dissipated; by contrast, as the initial wave amplitude is increased, the wave packet remains broader, achieves a lower maximum further away from the critical level, and decays less rapidly after the maximum has been reached. The corresponding changes in the mean wind are generally similar to those of the wave packet, with the addition of a small residual value due to dissipation. The interaction between the waves and the mean wind is also studied in the absence of any initial wind shear. The, results demonstrate a transfer of energy to the mean wind and a consequent decay in the amplitude of the wave.