These videos depict solitary waves or solitons at the interface of a buoyant viscous fluid conduit created by a "pulse" of additional fluid. The geometry of soliton interaction depends on the sizes of the two solitons. Video (except the colored ones) has been rotated 90 degrees, sped up, and aspect ratios have been changed. The videos titled "Single soliton closed streamlines" and "Solitons transfer fluid" are rotated 90 degrees and are in real time with a 1:1 aspect ratio. Associated paper.
Dispersive shock waves in a viscous fluid conduit are created by ramping up the injection rate to a sustained, larger value. Wavebreaking (gradient catastrophe) eventually occurs, leading to the spontaneous emergence of coherent, rank-ordered, expanding, nonlinear oscillations. For large jumps in the injection rate, the trailing edge envelope can propagate opposite to the direction of fluid flow upward. Video has been rotated 90 degrees, sped up, and aspect ratios have been changed. Associated theory and experiment.
Dispersive Hydrodynamics of Viscous Fluid Conduits
Dispersive hydrodynamics encompasses the large scale dynamics of dissipationless, dispersive fluids. The video depicts the overtaking interaction of a soliton and a dispersive shock wave. The image above is a space-time snapshot of the entire video (a contour plot of the experimental conduit amplitude in space-time), showing that the soliton is actually decelerated or refracted by the dispersive shock wave. Associated experiment.