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Dispersive shock waves and solitons are fundamental nonlinear excitations indispersive media, but dispersive shock wave studies to date have been severelyconstrained. Here we report on a novel dispersive hydrodynamics testbed: theeffectively frictionless dynamics of interfacial waves between two highcontrast, miscible, low Reynolds' number Stokes fluids. This scenario isrealized by injecting from below a lighter, viscous fluid into a column filledwith high viscosity fluid. The injected fluid forms a deformable pipe whosediameter is proportional to the injection rate, enabling precise control overthe generation of symmetric interfacial waves. Buoyancy drives nonlinearinterfacial self-steepening while normal stresses give rise to dispersion ofinterfacial waves. Extremely slow mass diffusion and mass conservation implythat the interfacial waves are effectively dissipationless. This enables highfidelity observations of large amplitude dispersive shock waves in thisspatially extended system, found to agree quantitatively with a nonlinear waveaveraging theory. Furthermore, several highly coherent phenomena areinvestigated including dispersive shock wave backflow, the refraction orabsorption of solitons by dispersive shock waves, and the multi-phase mergingof two dispersive shock waves. The complex, coherent, nonlinear mixing ofdispersive shock waves and solitons observed here are universal features ofdissipationless, dispersive hydrodynamic flows.

Observation of dispersive shock waves, solitons, and their interactions in viscous fluid conduits