A numerical study on nonresonant interactions of gravity waves in a compressible atmosphere

Abstract

Applying a second‐order numerical scheme, nonresonant interactions of gravity waves in a compressible atmosphere are investigated. The numerical results show that the nonresonant interaction of the gravity waves does occur, and an apparent energy exchange among the interacting waves can be observed, which indicates that the gravity waves with different spatial and temporal scales can extensively interact. In the nonresonant interaction, the wave energy generally tends to transfer from the primary wave with the highest frequency to the secondary and excited waves, which is different from that in the resonant interaction. Under the same initial energy of the secondary wave, the final energy of the excited wave is almost proportional to the initial energy of the primary wave. When the initial energies of the primary waves are identical, the final energy of the excited wave increases slowly with the increasing initial energy of the secondary wave. Similar to that in the resonant interaction, in the nonresonant interaction, wave vector and frequency of the excited wave show temporal variability. The wave vectors of the interacting triad do not satisfy the matching conditions which should be obeyed in the weak interaction theory. We also investigate the effects of the background wind field and viscous dissipation on the nonresonant interaction. The positive and negative background winds show tendencies to strengthen and weaken the wave energy transfer, respectively. This also differs from the weak interaction theory, in which only a Doppler shift can be caused. The primary effect of the viscosity is to dissipate the energy of the interacting waves. The viscosity can hardly prevent the nonresonant excitation, suggesting that the restriction of amplitude threshold on the interaction in the presence of viscosity predicted by the weak interaction approximation seems to be rather loose. As in the resonant interaction, the principal energy exchange is finished before the waves depart from each other, which indicates that the interacting characteristic time does exist in the nonresonant interaction. The characteristic time and evolutions of wavelength and intrinsic frequency for the excited wave are insensitive to the small initial wave amplitudes and Gaussian packet widths of the interacting waves, horizontal background wind field, and viscosity. However, the characteristic time is relevant to the wavelengths of the interacting waves.