Applicability of weakly nonlinear theory for planetary-scale flows

The relevance of isolated resonant triad interactions for the dynamics of the large-scale atmospheric circulation is investigated.
This is done within the context of the barotropic vorticity equation on the sphere. The equations governing the dynamics of a resonant triad on the sphere are of the same form as those on the beta-plane.
They can be solved analytically in terms of elliptic integrals ; giving a periodic vacillation of the amplitudes of the waves participating in the triad. The vacillation period depends on the total energy of the triad and on the initial energy distribution within the triad.
This dependence is investigated numerically. It is investigated whether or not, for realistic energy distributions, there exists a time-scale for which the resonant interactions within the triad dominate over the interactions of the triad components with the rest of the spectrum.