Author/Authors :
CARLOS F. M. RAUPP ، نويسنده , , PEDRO L. SILVA DIAS، نويسنده ,
Abstract :
In this paper we explore some dynamical features on the non-linear interactions among equatorial waves. The shallowwater
equation model with the equatorial β-plane approximation is used for this purpose. The Galerkin method is
applied to the governing equations with the basis functions given by the eigensolutions of the linear problem. From the
phase space expansion of two particular integrals of motion of the system, quadratic to lowest order, some constraints
are obtained which the coupling coefficients must satisfy in order to ensure the invariance of such integrals. From the
numerical evaluation of the coupling coefficients, these constraints are used to determine the possible resonant triads
among equatorial waves. Numerical integrations of the resonant three-wave problem show that the energy of the waves
in a resonant triad evolves periodically in time, with the period and amplitude of the energy oscillations dependent on
the magnitude of the initial amplitudes of the waves and the way in which the initial energy is distributed among the
triad components. The high-frequency modes are found to be energetically more active than the low-frequency modes.
The latter tend to act as ‘catalytic’ components in a resonant triad. Integrations of the problem of two resonant triads
coupled by a single mode point out the importance of gravity waves in the intertriad energy exchanges, suggesting the
significance of these modes in the redistribution of energy throughout the atmospheric motion spectrum. The results
also show that the intertriad energy exchanges provided by the highest frequency mode of two triads occur in a longer
time-scale than the intratriad interactions. Therefore, these results also suggest the importance of the high-frequency
modes in the generation of the low-frequency variability (intraseasonal and even longer term) of the atmospheric
flow.