A numerical study on the propagation and evolution of resonant interacting gravity waves

Abstract

Starting from the nonrotating, fully nonlinear basic atmospheric kinetic equations, the nonlinear propagation and evolution of resonant interacting gravity wave packets with small initial amplitudes in a two‐dimensional compressible atmosphere have been simulated. The complete nonlinear resonant interaction process of the gravity wave packets is exhibited. The numerical results show that a downward propagating gravity wave is excited by two up‐going gravity waves initially due to the resonant interaction, and the wavelength of the excited gravity wave decreases with time. During the whole nonlinear propagation and evolution, although the total wave energy for the interacting triad is almost conservative, obvious wave energy exchange among the three interacting gravity waves is observed. Wave energy tends to transfer from the wave with larger amplitude to that with smaller amplitude, and this energy transfer trend seems to be independent of the initial wave energies of the interacting waves. A detailed numerical analysis shows that when a gravity wave is excited by resonant interaction, its energy continuously grows up from 0 J to a considerable level (5.44 × 105 J). This process is irreversible rather than periodic and will be finished within a characteristic time (15 hours for the presented case). More simulation examples are also carried out to study the effects of the small initial amplitudes and wavelengths on the energy exchange, which shows that although the characteristic time is not sensitive to the small initial amplitudes, it depends on the wavelengths, and both the initial amplitudes and wavelengths can affect the net wave energy exchange of the resonant interaction.