This paper explores a possible explanation for the relatively high magnitude of the Mixed Rossby-Gravity wave detected in the tropical Atlantic sector, based on the non-linear interaction between Rossby and Kelvin waves. A spectral non-linear shallow water model is used to explore the role of the interaction among the tropical waves.

The convective activity in the Amazon Basin presents a well defined annual cycle, shifting from the northern and northwestern parts of the basin in July/August to the central and southern edges of the Amazon in September/October and returning to the northern areas in May/June. Apart from the well defined annual cycle, higher frequency variability is also detected in the convection in Amazon region up to the very prominent diurnal variation of convection. Theoretical studies have explored the role of the heat source of tropical S. America in the generation of Rossby, Mixed Rossby-Gravity, Kelvin and Gravity waves for the maintenance of the observed circulation patterns, such as the upper tropospheric anticyclonic circulation known as the Bolivian High. The theoretical studies also indicate that the diurnal forcing of the convection triggers substantial energy in the Kelvin modes. Mixed Rossy Waves are also generated by the stationary heat source. However, observational studies of the equatorial waves, based on satellite information and global reanalysis have indicated a significant correlation between the classical equatorial waves and convective activity and organization. In particular, a significant signal of the mixed Rossby-Gravity wave with period of the order of a few days was identified.

The non-linear shallow water model is solved in the spectral form using the normal modes of the linearized version about a basic state at rest (i.e., the Matsuno waves) with a mass source which has a stationary component and a highly transient signal associated to the diurnal variation of convection. The diurnal signal of the convection is crucial for the development of Kelvin waves. The integration of the model shows that the Kelvin waves are responsible for a large conversion of energy from the Rossby waves, which are predominantly excited by the stationary component of the forcing, to the Mixed Rossby-Gravity waves with period of the order of 4 days and wavelength of approximately 3000km. Much more significant interhemispheric energy propagation is also detected in the non-linear solution which also clealy shows signs of vacillation.