Controlling Dispersive Hydrodynamic Wavebreaking in a Viscous Fluid Conduit

Abstract

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.