We examine the evolution of three-gravdy-wave interactions, with one initaly much stronger Ihun the other two, in a dissipative atmosphere, The characteristic time is used as an essential lime ca e for depicting the interactions. In the absense of viscosity, the solutions of the lineatized interaction equations, viz., the paramettic instability, give a good description for the evolution of secondary waves up to one-hail ol the characteristic time Beyond this time, the linear solutions are invalid; the evolution must be obtained by solving the complete interaction equations For given initial wave amplitudes, the characteristic time increases with the increasing wavelength of the primary wave; thus the criterion for the validity of resonant interaction approximation may be better satisfied The viscous dissipation makes the characteristoc time larger, and when severe enough a porlion oftbe seuondary waves, particularly at high wavenumbers, may fail to interacl with the primary wave effectively Additionally. the maxima of the energy densities for the secondary wavve are smaller than those in the absence of viscosity. In the ease of a significalt frequeney mismatch, only a fraction of the primary wave energy lakes part in the hlterchange Copyright.

By amdyzing tile resutts of the numerical sinlulations ol nonlinear propagation of three Gaussian gravlly-wave packms in isothermal atmosphere individually, tile nonlinear effects on the characteristics of glavity waves are studied quantitatively. The analyses show that during the nonlinear propagation of gravity wave packets the mean fows are accelerated and the vertical wavelengths show clear reduction due to non-linearity 011 the other band, though nonlinear effects exist, the time variations of the fi'equencies of gravity wuve packets are close to those derived from the dispersion relation and the amplitude and phase relations of wave-associated disturbance components are consistent with the pledictions of the polarization rchttion of giavity waves. This indicates that the dispersion and polarization rehltions based on the linear grawty wave theory can be applied extensively in the nonlinear region