A numerical study on matching relationships of gravity waves in nonlinear interactions

• Published in: Science China. Earth sciences Vol. 56; no. 6; pp. 1079 - 1090
• Main Authors: Huang, KaiMing, Zhang, ShaoDong, Yi, Fan
• Format: Journal Article
• Language: English
• Published: Heidelberg SP Science China Press 01.06.2013; Springer Nature B.V
• Subjects: Atmospheric sciences; Earth and Environmental Science; Earth Sciences; Excitation; Geophysics; Gravity; Gravity waves; Matching; Nonlinearity; Numerical analysis; Perturbation methods; Propagation; Research Paper; Resonant interactions; Wavelengths; Wavenumber; 匹配关系; 匹配条件; 数值研究; 重力波; 非共振激发; 非共振相互作用; 非线性数值方法; 非线性相互作用; gravity wave; detuning degree of interaction; matching condition; nonlinear interaction
• ISSN: 1674-7313; 1869-1897
• DOI: 10.1007/s11430-012-4522-0

Applying a fully nonlinear numerical scheme with second-order temporal and spatial precision, nonlinear interactions of grav- ity waves are simulated and the matching relationships of the wavelengths and frequencies of the interacting waves are dis- cussed. In resonant interactions, the wavelengths of the excited wave are in good agreement with the values derived from sum or difference resonant conditions, and the frequencies of the three waves also satisfy the matching condition. Since the inter- acting waves obey the resonant conditions, resonant interactions have a reversible feature that for a resonant wave triad, any two waves are selected to be the initial perturbations, and the third wave can then be excited through sum or difference reso- nant interaction. The numerical results for nonresonant triads show that in nonresonant interactions, the wave vectors tend to approximately match in a single direction, generally in the horizontal direction. The frequency of the excited wave is close to the matching value, and the degree of mismatching of frequencies may depend on the combined effect of both the wavenumber and frequency mismatches that should benefit energy exchange to the greatest extent. The matching and mismatching rela- tionships in nonresonant interactions differ from the results of weak interaction theory that the wave vectors are required to satisfy the resonant matching condition but the frequencies are permitted to mismatch and oscillate with amplitude of half the mismatching frequency. Nonresonant excitation has an irreversible characteristic, which is different from what is found for the resonant interaction. For specified initial primary and secondary waves, it is difficult to predict the values of the mismatching wavenumber and frequency for the excited wave owing to the complexity.