Results on the nonlinear behavior of the Rayleigh–Taylor instability and consequent development of shear flow by the shear instability [Phys. Fluids B4, 488 (1992)] are presented. It is found that the shear flow is generated at sufficient amplitude to reduce greatly the convective transport. For high viscosity, the time‐asymptotic state consists of an equilibrium with shear flow and vortex flow (with islands, or ‘‘cat’s eyes’’), or a relaxation oscillation involving an interplay between the shear instability and the Rayleigh–Taylor instability in the presence of shear. For low viscosity, the dominant feature is a high‐frequency nonlinear standing wave consisting of convective vortices localized near the top and bottom boundaries. The localization of these vortices is due to the smaller shear near the boundary regions. The convective transport is largest around these convective vortices near the boundary and there is a region of good confinement near the center. The possible relevance of this behavior to the H mode and edge‐localized modes (ELM’s) in the tokamak edge region is discussed.