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We describe and illustrate a mechanism whereby convective aggregation and eastward propagating equatorial disturbances, which are similar in some respects to the Madden–Julian Oscillation (MJO), arise. We construct a simple explicit system consisting only of the shallow‐water equations plus a humidity variable; moisture enters via evaporation from a wet surface, is transported by the flow and removed by condensation, thus producing an anomaly in the height field. For a broad range of parameters the system is excitable even when linearly stable, with condensation producing convergence and gravity waves that, acting together, trigger more condensation. On the equatorial β‐plane the convection first aggregates near the Equator, generating patterns related to those encountered in the Matsuno–Gill problem. However, the pattern is unstable and more convection is triggered on its eastern edge, leading to a self‐sustaining precipitating disturbance that progresses eastward. The propagation is eastward because the warm, moist converging air from the east induced by the Matsuno–Gill pattern is more convectively unstable than the converging air from the west. The pattern is confined to a region within a few deformation radii of the Equator, as here the convection can create the convergence needed to organize itself into a self‐sustaining pattern; thus, smaller values of the beta parameter give rise to a wider disturbance. Formation of the disturbance preferentially occurs where the surface is warmer, and sufficient time (typically a few tens of days) must pass before conditions arise that enable the disturbance to reform, a well‐known characteristic of the MJO. The speed of the disturbance depends on the efficiency of evaporation and the heat released by condensation, and is typically a few metres per second, much less than the Kelvin wave speed.

Convective organization and eastward propagating equatorial disturbances in a simple excitable system