Large Amplitude Solitary Waves and Dispersive Shock Waves in Conduits of Viscous Liquids
Mark Hoefer
Applied Mathematics, University of Colorado Boulder
Date and time:
Tuesday, September 2, 2014 - 3:15pm
Location:
Bechtel Collaboratory in the Discovery Learning Center (DLC)
Abstract:
(First of two talks. Will run approximately half an hour. See printable announcement for full details).
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).