Buoyant plumes often pulsate, or puff, at a characteristic frequency that depends on the Richardson number. In many engineering and natural applications, however, interactions between two or more plumes can substantially affect the puffing frequency. In this study, we use numerical simulations to investigate how the plume width, $W$, and the separation between two plumes, $S$, affect the puffing frequency. The plumes are formed by injecting helium into ambient air, and we perform the simulations in two spatial dimensions to identify scaling laws in the limits of large and small $S$. We find that the global dependence on $S$ closely matches that observed in reacting three-dimensional (3D) plumes, indicating that the plume dynamics are primarily connected to the presence of buoyant forces, regardless of the source of buoyancy. There is a critical value of $S$ at which the puffing frequency changes abruptly but, in contrast to 3D reacting plumes, this critical value is independent of $W$ for the present two-dimensional plumes. Ultimately, we find that the nonlinear decrease in puffing frequency with increasing spacing can be represented by a scaling law that depends only on $S/W$ and the inlet Richardson number. These results allow us to identify four regimes of puffing behavior, corresponding to merged, strongly interacting, weakly interacting, and noninteracting plumes.

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• Flow instability
• Shear flows
• Synchronization transition
• Transition to turbulence