Applying a fully nonlinear numerical scheme with second-order temporal and spatial precision,nonlinear interactions of gravity waves are simulated and the matching relationships of the wavelengths and frequencies of the interacting waves are discussed.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 interacting 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 resonant 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 relationships 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.
The characteristics of high-latitude planetary waves (PWs) in the troposphere and lower stratosphere (TLS) are studied by using the data from radiosonde observations during 1998 to 2006 at three Alaskan stations in USA (Nome, 64.50°N, 165.43°W; McGrath, 62.97°N, 155.62°W; Fairbanks, 64.82°N, 147.87°W). It is found that strong PWs exist in two regions. One is around tropopause, and the other is in the polar night jet (PNJ) in winter. The PW activities are rather intermittent, and their lifetimes are no longer than two months. Among three perturbation components in zonal and meridional winds and temperature, the temperature disturbance amplitude is the smallest, and the amplitude for the meridional wind component the largest. Around the tropopause, quasi 5-, 10-, and 16-day PW activities can be observed simultaneously. Among these PW components, the quasi 5-day and 10-day PW are the weakest and strongest, respectively. Moreover, PWs around the tropopause are complex and no obvious season variability can be observed. However, in the PNJ, the higher region, only obvious quasi 10-day and 16-day PWs remain, with smaller amplitudes than those around the tropopause. And significant PWs in the PNJ occur only in winter. By calculating the refractive index for PWs, it is found that there is a persistent reflection layer around 11 km, which is thick in summer and becomes thin or even disappears in winter, revealing that PWs in the stratosphere can only occur in winter. PWs in the 2003/2004 winter at the three stations are analyzed in detail. It is found that for the focused observation duration, the quasi 10-day and quasi 16-day waves exist mainly in the troposphere and stratosphere, respectively. The quasi 10-day wave is a standing wave in the vertical direction, with vertical wavelength about 12 km in the temperature component and larger than 26 km in the meridional component. Moreover, the tropospheric quasi 10-day wave propagates westward with the zonal numbers between 2 and 4. The quasi 16-day wave is also a stand
WANG Rui1,2,3, ZHANG ShaoDong1,2,3 & YI Fan1,2,3 1 School of Electronic Information, Wuhan University, Wuhan 430079, China
