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The asymptotic method of multiple time-scales is used to investigate the nonlinear interactions among equatorial waves in an equatorial β-plane adiabatic primitive equation atmospheric model in isobaric coordinates. The equatorial Rossby, mixed Rossby-gravity, Kelvin and inertio-gravity waves, with several vertical structures, are obtained as the leadingorder solution. From the solvability condition of the problem, a reduced model governing the weakly nonlinear interaction of the waves in a particular resonant triad was obtained. The total energy conservation of the leading-order solution of the original model equations implies that the sum of the coupling coefficients in any resonant triad must be zero. Using a graphical approach, we determined some resonant triads involving equatorially trapped baroclinic waves and barotropic Rossby waves having large mid-latitude amplitude. Two particular interactions deserve special attention because of their strong coupling and their possible relation to observed features in the atmospheric circulation. One is characterized by a first baroclinic mode structure mixed Rossby-gravity wave interacting with a barotropic Rossby wave with the second gravest meridional mode, both having the same wavenumber, through a zonally symmetric geostrophic mode with the same vertical structure as the Yanai wave and having the n = 1 meridional mode. The other triad is composed of a zonal wavenumber-1 Kelvin wave, a zonal wavenumber-2 mixed Rossby-gravity wave, both with the first baroclinic mode vertical structure, and a barotropic zonal wavenumber-3 Rossby wave having the second gravest meridional mode. The barotropic Rossby waves in these two triad interactions have significant projection onto middle and higher latitudes. The integration of the triad equations for these particular interactions shows that, for the initial mode amplitudes characterizing typical magnitudes of atmospheric flow perturbations, the modes in the first triad usually exchange energy on intraseasonal time-scales, while the modes in the second triad exchange energy on either intraseasonal or semi-annual time-scale, depending on the initial condition. The implications of the results for the dynamics of tropics-extratropics interaction on low-frequency time-scale are discussed.

"Interação não-linear entre ondas atmosféricas: um possível mecanismo para a conexão trópicos-extratrópicos em baixa-frequência"