[en] The nonlinear behavior of the 2D Benard problem with periodic boundary conditions in the horizontal direction, a model for interchange modes in the tokamak edge region, has been studied with the aim of understanding the L-H transition and ELMS. The results show a complex interplay between vortices driven by the Rayleigh-Taylor instability and shear flow which is driven by the vortices and which causes their decay. In this paper the authors study the transition from the low Rayleigh number (Ra) regime to the high Ra regime. For the former, vortex flow and shear flow coexist, possibly with slow relaxation oscillations. In the high Ra regime there are vortices localized near the upper and lower boundaries with a shear flow in between. As Ra is decreased, these vortices broaden, eventually overlapping, causing self-consistent Lagrangian chaos. This onset of chaos is responsible for the transition to the low Ra regime. In the low Ra regime, on the other hand, the relaxation oscillations are on a much slower time scale than the eddy turnover time and the Lagrangian behavior is described by separatrix crossing