Large Amplitude Solitary Waves and Dispersive Shock Waves in Conduits of Viscous Liquids


A dispersive shock wave (DSW) represents the combination of solitary and linear dispersive wave phenomena into one coherent structure. DSWs are therefore fundamental nonlinear structures that can occur in any conservative hydrodynamic setting, e.g., superfluids, “optical fluids” as well as classical fluids such as shallow water. Experimental studies of DSWs in all media have been restricted by inherent physical limitations such as multi-dimensional instabilities, difficulties in capturing dynamical information, and, eventually, dissipation. These limit DSW amplitudes, evolution time, and spatial extent. In this talk, a new medium is proposed in which to study DSWs that overcomes all of these difficulties, allowing for the detailed, visual investigation of dispersive hydrodynamic phenomena. The vertical evolution of the interface between a buoyant, viscous liquid conduit surrounded by a miscible, much more viscous fluid exhibits nonlinear self-steepening (wave breaking), dispersion, and negligible dissipation. First, it will be shown experimentally and theoretically that the two-soliton interaction geometry can be classified into three distinct types, extending Peter Lax’s famous result for the weakly nonlinear Korteweg-de Vries equation into the strongly nonlinear regime. Then, DSW experiments and novel DSW-soliton interaction behaviors will be presented and compared with modulation theory. The talk will cover multiple scales, from the microscopic (Navier-Stokes), mesoscopic (interfacial conduit equation), and macroscopic (Whitham modulation equations), to the truth (experiments).

Sep 2, 2014 3:30 PM — 4:30 PM
Bechtel Collaboratory, Discovery Learning Center
Engineering Center, University of Colorado at Boulder, Boulder, CO 80309

University of Colorado Boulder