重力波非共振激发的数值研究

A numerical study on gravity wave excited through nonresonant interaction

应用二阶算子分裂格式,采用全非线性模式,对可压大气中重力波波包非共振激发进行数值模拟和分析.研究表明:两个向上传播的重力波波包,通过非共振相互作用,也能激发出一个向下传播的重力波波包.生成波的能量几乎正比于主波的能量,也随次波的能量增大而增大.能量传递方向主要表现为从高频的主波向次波和生成波转移,这与共振相互作用不完全相同.非共振作用的特征时间由主次波的初始位置和波长频率决定,与主次波的初始振幅无关.生成波的波矢量并不严格满足弱非线性相互作用理论预言的波矢量匹配条件,而且生成波的波长和频率在传播的过程中会随时间发生变化,这表明了弱非线性相互作用理论的局限性.

By using a 2nd order operator-splitting scheme and taking a fully nonlinear model, numerical simulation of gravity wave excited through nonresonant interaction in a compressible atmosphere is carried out. The results show that a downward propagating gravity wave packet can be excited by two up-going gravity wave packets owing to the nonresonant interaction. The energy of the excited wave is almost proportional to the energy of the primary wave, and increases slowly with initial energy of the secondary wave growing up, too. Wave energy tends to transfer mainly from the primary wave with highest frequency to other two waves, which isn＇t completely consistent with the resonant interaction. The characteristic time of the nonresonant interaction depends on the initial positions, wavelengths and frequencies of the primary and secondary waves, however, is independent of their initial amplitudes. The wave vector of the excited wave doesn＇ t strictly satisfy the wave vector matching condition which is predicted by the weakly nonlinear interaction theory. Moreover, the wavelength and frequency of the excited wave are found to vary with time in the propagation. These indicate the weakly nonhnear interaction theory is limited to some extent for the nonresonant interaction.