This paper considers the effects of turbulent plumes with time-varying buoyancy released from a point source in a confined region. Attention is concentrated on the case of cyclically varying buoyancy sources. After many cycles, an asymptotic regime is created in which the fluid away from the plume is stably stratified. During the statically unstable phase of the cycle, the plume extends farther and farther into the fluid, spreading out horizontally at a level determined predominantly by the density in the plume at that depth. For about one half of this phase the plume extends almost the full depth of the container and then retreats back toward the source.