Nonlinear Internal Gravity Waves and Their Interaction with the Mean Wind

Abstract

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 dissipa...