Spectral energy transfer of atmospheric gravity waves through sum and difference nonlinear interactions

Abstract

Abstract. Nonlinear interactions of gravity waves are studied with a two-dimensional, fully nonlinear model. The energy exchanges among resonant and near-resonant triads are examined in order to understand the spectral energy transfer through interactions. The results show that in both resonant and near-resonant interactions, the energy exchange between two high frequency waves is strong, but the energy transfer from large to small vertical scale waves is rather weak. This suggests that the energy cascade toward large vertical wavenumbers through nonlinear interaction is inefficient, which is different from the rapid turbulence cascade. Because of considerable energy exchange, nonlinear interactions can effectively spread high frequency spectrum, and play a significant role in limiting wave amplitude growth and transferring energy into higher altitudes. In resonant interaction, the interacting waves obey the resonant matching conditions, and resonant excitation is reversible, while near-resonant excitation is not so. Although near-resonant interaction shows the complexity of match relation, numerical experiments show an interesting result that when sum and difference near-resonant interactions occur between high and low frequency waves, the wave vectors tend to approximately match in horizontal direction, and the frequency of the excited waves is also close to the matching value.

Nonlinear interaction of gravity waves in a nonisothermal and dissipative atmosphere

“…Even so, we can note an interesting phenomenon that the horizontal wavelength of wave 3 equals the matching wavelength of 36.52 km, which indicates that the interacting waves meet the matching condition in the horizontal scale. In an isothermal atmosphere, the nonresonant wave triad mismatches in the vertical scale but matches in in the horizontal scale, and their frequencies tend to match, moreover, such a relationship is explained based on the energy exchange in the nonresonance (Huang et al, 2012). Therefore, the match relationship of the interaction in a nonisothermal atmosphere is consistent with those in an isothermal atmosphere.…”

“…conditions while nonresonant excitation is not so (Huang et al, 2012). Significant third-order resonance of gravity waves can arise in the atmosphere, which occurs through direct interaction of waves that satisfy the corresponding third-order resonant conditions instead of through an intermediate forced mode involved in interaction suggested by a previous study (Huang et al, 2013c).…”

“…Dominant sources of gravity waves are convective storm, airflow over topography, wind shear and geostrophic adjustment in the lower atmosphere . In the MLT, body forcing accompanying wave dissipation and breaking, wave-wave interaction and auroral heating can locally generate upward and downward gravity waves (Snively and Pasko, 2003;Vadas et al, 2003;Huang et al, 2012;Vadas and Liu, 2009). Satellite (Preusse et al, 2009;Alexander and Teitelbaum, 2011) and ground-based observations (Tsuda et al, 1990;Hickey et al, 1998;Vincent and Alexander, 2000;Dou et al, 2010;Yue et al, 2013;Zhang et al, 2013) show that small scale gravity waves have also broad temporal and spatial scales.…”

“…Satellite (Preusse et al, 2009;Alexander and Teitelbaum, 2011) and ground-based observations (Tsuda et al, 1990;Hickey et al, 1998;Vincent and Alexander, 2000;Dou et al, 2010;Yue et al, 2013;Zhang et al, 2013) show that small scale gravity waves have also broad temporal and spatial scales. When these gravity waves with different scales interact with each other, a sum or difference new wave is usually excited (Klostermeyer, 1984(Klostermeyer, , 1990Widdel et al, 1994;Rüster, 1997;Wüst and Bittner, 2006;Huang et al, 2009Huang et al, , 2012, while numerical experiments with GCM presented by Chang et al (2011) demonstrate that in interactions among large scale planetary waves and tides, both sum and difference new waves are generated, and evidence of sum and difference secondary waves is also observed in radar measurements Beard et al, 1997Beard et al, , 1999Pancheva, 2006;Huang et al, 2013b), moreover, tidal modulation due to the beat is generally clear (Teitelbaum and Vial, 1991;Beard et al, 1997Beard et al, , 1999Huang et al, 2013b). Hence, relative to interactions among planetary waves and tides, nonlinear interaction of gravity waves shows some special characteristics.…”

Third‐order resonant interaction of atmospheric gravity waves

“…Because of spatially localized interaction for gravity wave packets, energy transfer is permanent rather than periodic in the weak interaction theory [ Huang et al ., ], and is completed in the several periods of the primary waves [ Vanneste , ]. Resonant excitation is reversible due to the satisfaction of the resonant conditions while nonresonant excitation is not so [ Huang et al ., ]. In nonresonant interaction, all the interacting waves obey the dispersion relation of gravity waves [ Huang et al ., , ], which is different from the result in the weak interaction theory [ Yeh and Dong , ; Yi and Xiao , ].…”