Large-scale convective storms are a common phenomenon in Jupiter's atmosphere. They are apparent in ground-based and spacecraft images and may strongly affect the dynamics of the global atmosphere as well as the energy transport in the meteorological layer. In this paper we analyze the outburst of a large convective storm system (core ~5000 km) in the South Equatorial Belt (SEB) that was observed at high spatial and temporal resolution by the Voyager 1 spacecraft in 1979. We use a two-dimensional (2-D) model to study the interaction between cloud material brought up by moist convection and the environmental wind. Aided by previous 3-D models of Jovian storms, we can draw several qualitative and quantitative conclusions. The evolution of this storm can be characterized by three phases: (1) onset of the perturbation, well reproduced by the growth of a single-cell storm; (2) an expanding phase in which the number of convective cells increases to ~200, with updraft velocities limited to 50 m/s; and (3) a relatively sudden suppression of the convective activity leading to the disruption of large structures by the environmental wind. Furthermore, we interpret the observations of the inner bright core as a well-defined anticyclonic vortex, with darker cloud material preferentially left southwest of the system. Finally, we show that ~1016 W are released by such a storm over its life cycle of 12 days and that the direct formation of a large-scale anticyclonic vortex after the moist convective source has been removed is prevented by the environmental wind shear.