Solitary waves on conduits of buoyant fluid in a more viscous fluid

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Abstract
Fluid of a lower density and viscosity can buoyantly rise through a viscous fluid through conduits that support simple pipe flows. The conduits also support solitary waves which exhibit near soliton behavior. Laboratory experiments on the characteristics of the solitary waves and their interactions have been conducted and compared with theory. The observations of shape and phase speed of individual waves show good agreement with the theoretical predictions. Large amplitude waves traveled slightly faster than the theoretical predictions. The discrepancy is probably due to higher order effects associated with wave slope not accounted for in the theory. Individual wave characteristics (shape, amplitude and speed) were very nearly preserved after collision with another wave. A phase jump of each wave was the main consequence of an interaction. The larger (faster) waves increased in amplitude by an average of 5 percent after collision and their phase speeds decreased by an average of 4 percent. The small wave was unchanged. Numerical solutions overpredicted the magnitude of the observed phase jumps by about 40 percent when compared to the experiments. It is also shown theoretically and confirmed experimentally that the solitary waves have closed streamlines in a frame moving with the wave. Thus, transport of isolated packets of fluid over large distances will occur. Wave interactions result in the transfer of trapped fluid between the interacting waves.

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