A linear shallow water model is used to simulate the evolution of mixed Rossby-gravity (MRG) waves in background states representative of the convective phase of the Madden-Julian oscillation (MJO). Initial MRG wave structures are obtained analytically. The MJO basic state is defined by the steady response of the tropical atmosphere to localized heating. Results from the simulations reveal that variations in the background flow play a significant role in the evolution of the MRG waves. When the basic state is symmetric about the equator, the MRG wave amplifies within the convergent region of the background flow and the ensuing development remains symmetric. When the heating is asymmetric, both the basic state and the MRG wave evolution exhibit significant asymmetries. Prominent features of this simulation are the development and growth of a series of small-scale, off-equatorial eddies that resemble tropical-depression-type disturbances.
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Aiyyer et al. (2003) studied this question.