Observation of Dispersive Shock Waves, Solitons, and Their Interactions in Viscous Fluid Conduits

Michelle D. Maiden, Nicholas K. Lowman, Dalton V. Anderson, Marika E. Schubert, and Mark A. Hoefer
Phys. Rev. Lett. 116, 174501 – Published 28 April 2016
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Abstract

Dispersive shock waves and solitons are fundamental nonlinear excitations in dispersive media, but dispersive shock wave studies to date have been severely constrained. Here, we report on a novel dispersive hydrodynamic test bed: the effectively frictionless dynamics of interfacial waves between two high viscosity contrast, miscible, low Reynolds number Stokes fluids. This scenario is realized by injecting from below a lighter, viscous fluid into a column filled with high viscosity fluid. The injected fluid forms a deformable pipe whose diameter is proportional to the injection rate, enabling precise control over the generation of symmetric interfacial waves. Buoyancy drives nonlinear interfacial self-steepening, while normal stresses give rise to the dispersion of interfacial waves. Extremely slow mass diffusion and mass conservation imply that the interfacial waves are effectively dissipationless. This enables high fidelity observations of large amplitude dispersive shock waves in this spatially extended system, found to agree quantitatively with a nonlinear wave averaging theory. Furthermore, several highly coherent phenomena are investigated including dispersive shock wave backflow, the refraction or absorption of solitons by dispersive shock waves, and the multiphase merging of two dispersive shock waves. The complex, coherent, nonlinear mixing of dispersive shock waves and solitons observed here are universal features of dissipationless, dispersive hydrodynamic flows.

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  • Received 31 December 2015

DOI:https://doi.org/10.1103/PhysRevLett.116.174501

© 2016 American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Authors & Affiliations

Michelle D. Maiden1, Nicholas K. Lowman2, Dalton V. Anderson1, Marika E. Schubert1, and Mark A. Hoefer1,*

  • 1Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309, USA
  • 2Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695, USA

  • *hoefer@colorado.edu

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Vol. 116, Iss. 17 — 29 April 2016

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