Resonant and nonresonant wave‐wave interactions in an isothermal atmosphere

Abstract

We consider the weakly nonlinear three‐wave interactions in an isothermal atmosphere. The mutual interactions among the three linear branches of dynamical‐thermodynamical atmospheric motions (gravity waves, acoustic waves, and vortical motions) are investigated. In addition to the resonant case, nonresonant interactions are also considered. On the basis of the analytical solution of the linearized wave‐amplitude equation with possible existence of a frequency mismatch, the resonance surface, the interaction domain, and growth time in three‐dimensional geometry in k‐space in various cases have been calculated and some numerical results are given. It is found that the nonresonant interaction can be very important, especially when a gravity wave and two vortical modes of motions interact as a nonresonant trio. The energy transfer from the gravity wave to vortical motions might limit the growth of the gravity wave amplitude and hence might provide a reasonable mechanism for gravity waves to saturate in the middle atmosphere.

Nonlinear interaction of gravity waves in a nonisothermal and dissipative atmosphere

“…Similarly, for the sake of examining the match relationship among interacting waves and exploring the dependence of energy exchange upon the detuning degree of interaction, previous numerical studies focused on resonant and nonresonant interactions in an isothermal atmosphere (Huang et al, 2009(Huang et al, , 2011(Huang et al, , 2013c, and only the effect of constant molecular kinematic diffusivity was investigated (Yi, 1999;Huang et al, 2007). Even so, numerical results based on fully nonlinear model indicate that the restriction of amplitude threshold on interaction in the presence of viscous dissipation seems to be rather loose, and all interacting waves still satisfy the dispersion relation (Huang et al, 2007), which is different from the prediction of theoretical study from the linearised equations (Dong and Yeh, 1988;Yeh and Dong, 1989;Yi and Xiao, 1997). This indicates that interaction of gravity waves is in need of nonlinear investigation.…”

“…The theoretical study predicts that there is an amplitude threshold on interaction in the presence of molecular viscous dissipation, which means that the atmospheric dissipation may prevent interaction for small amplitude waves. And if interaction takes place, the dissipation makes energy exchange time larger, at this case, interacting waves do not obey the dispersion relation any more (Dong and Yeh, 1988;Yeh and Dong, 1989;Yi and Xiao, 1997). Hereby, the dissipative effect on interaction in the MLT is believed to be important since the molecular kinematic diffusivity exponentially increases with height (Yi and Xiao, 1997;Yi, 1999).…”

“…Based on the linearised equations under the condition of weak nonlinear phenomena of waves in fluids, the properties of resonant and nonresonant interactions of oceanic and atmospheric internal gravity waves were extensively studied, and the effects of interaction on spectral energy transfer and universal spectrum formation were discussed (Phillips, 1960;Yeh and Liu, 1981;Müller et al, 1986;Inhester, 1987;Dong and Yeh, 1988;Fritts et al, 1992;Yi and Xiao, 1997;Stenflo and Shukla, 2009). Fritts et al (1992) presented general interaction equations and coefficients for resonant and nonresonant interactions of gravity waves in a compressible atmosphere with rotation and small wind shear.…”

Parametrization of momentum and energy depositions from gravity waves generated by tropospheric hydrodynamic sources

“…The value of u i is zero up to the altitude at which IGW becomes unstable, and u i is calculated using the semi-empirical model of Gavrilov and Yudin (1992) above this altitude. Several studies of nonlinear destruction of the primary IGW into secondary wave harmonics were made for resonant and nonresonant wave±wave interactions (Weinstock, 1982(Weinstock, , 1990Dong and Yeh, 1988;Rozenfeld, 1983;Sonmor and Klaassen, 1996). Some papers contain expressions for the eective coecients of turbulent viscosity produced by a spectrum of secondary wave harmonics generated by a primary IGW.…”

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

“…On the basis of the weak interaction approximation, many features and effects of resonant interaction of oceanic internal gravity waves have been acquired (Phillips, 1960;Bretherton, 1964;Hasselmann, 1966;Olbers, 1976;McComas and Bretherton, 1977;McComas and Müller, 1981;Müller et al, 1986). Subsequently, the properties of resonant and nonresonant interactions among atmospheric gravity waves have been extensively investigated (Dysthe et al, 1974;Liu, 1981, 1985;Klostermeyer, 1982Klostermeyer, , 1991Inhester, 1987;Dong and Yeh, 1988;Yeh and Dong, 1989), even in a sheared, dissipative and rotating atmosphere 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.…”