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The driven, cylindrical, free interface between two miscible, Stokes fluids with high viscosity contrast have been shown to exhibit dispersive hydrodynamics. A hallmark feature of dispersive hydrodynamic media is the dispersive resolution of wavebreaking that results in a dispersive shock wave. In the context of the viscous fluid conduit system, the present work introduces a simple, practical method to precisely control the location, time, and spatial profile of wavebreaking in dispersive hydrodynamic systems with only boundary control. The method is based on tracking the dispersionless characteristics backward from the desired wavebreaking profile to the boundary. In addition to the generation of approximately step-like Riemann and box problems, the method is generalized to other, approximately piecewise-linear dispersive hydrodynamic profiles including the triangle wave and N-wave. A definition of dispersive hydrodynamic wavebreaking is used to obtain quantitative agreement between the predicted location and time of wavebreaking, viscous fluid conduit experiment, and direct numerical simulations for a range of flow conditions. Observed space-time characteristics also agree with triangle and N-wave predictions. The characteristic boundary control method introduced here enables the experimental investigation of a variety of wavebreaking profiles and is expected to be useful in other dispersive hydrodynamic media. As an application of this approach, soliton fission from a large, box-like disturbance is observed both experimentally and numerically, motivating future analytical treatment.
We consider two physically and mathematically distinct regularization mechanisms of scalar hyperbolic conservation laws. When the flux is convex, the combination of diffusion and dispersion are known to give rise to monotonic and oscillatory travelin
Surface and interfacial weakly-nonlinear ring waves in a two-layer fluid are modelled numerically, within the framework of the recently derived 2+1-dimensional cKdV-type equation. In a case study, we consider concentric waves from a localised initial
We study a dispersive counterpart of the classical gas dynamics problem of the interaction of a shock wave with a counter-propagating simple rarefaction wave often referred to as the shock wave refraction. The refraction of a one-dimensional dispersi
We theoretically describe the quasi one-dimensional transverse spreading of a light pulse propagating in a nonlinear optical material in the presence of a uniform background light intensity. For short propagation distances the pulse can be described
Ubiquitous nonlinear waves in dispersive media include localized solitons and extended hydrodynamic states such as dispersive shock waves. Despite their physical prominence and the development of thorough theoretical and experimental investigations o