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

K M Huang,Z Li,S D Zhang,A Z Liu,F Yi

doi:10.5194/angeo-30-303-2012

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.

Highlights

Gravity waves are one of the most important waves in the middle and upper atmosphere and play a crucial role in determining large-scale circulation and thermal structure of the middle atmosphere because of their inherent ability to transport momentum and energy from one atmospheric layer to another (Lindzen, 1981; Holton, 1982; Vincent and Reid 1983; Fritts and Dunkerton, 1985)
By the numerical experiments of resonant and near-resonant triads, we exhibited the excitation of new waves in the sum and difference interactions and discussed the energy exchange among the spectral components
The nonlinear cascade toward increasing vertical wavenumbers is weak through the interaction; (2) the resonant excitation is reversible while the near-resonant excitation is not

Summary

Introduction

Gravity waves are one of the most important waves in the middle and upper atmosphere and play a crucial role in determining large-scale circulation and thermal structure of the middle atmosphere because of their inherent ability to transport momentum and energy from one atmospheric layer to another (Lindzen, 1981; Holton, 1982; Vincent and Reid 1983; Fritts and Dunkerton, 1985). The properties of resonant and nonresonant interactions among atmospheric gravity waves have been extensively investigated (Dysthe et al, 1974; Yeh and Liu, 1981, 1985; Klostermeyer, 1982, 1991; Inhester, 1987; Dong and Yeh, 1988; Yeh and Dong, 1989), even in a sheared, dissipative and rotating atmosphere (Fritts et al, 1992; Axelsson et al, 1996; Yi and Xiao, 1997), and in the uniform and nonuniform plasmas (Stenflo, 1994; Stenflo and Shukla, 2009) These theoretical studies provided essential understanding of nonlinear interactions of gravity waves.

Governing equations and numerical scheme

Initial background and perturbation

Sum and difference resonant interactions

Findings

Summary