Dissertation/Thesis Abstract

Dispersive Hydrodynamics in Viscous Fluid Conduits
by Maiden, Michelle Dorothy, Ph.D., University of Colorado at Boulder, 2019, 155; 13856836
Abstract (Summary)

Viscous fluid conduits provide an ideal system for the study of dissipationless, dispersive hydrodynamics. A dense, viscous fluid serves as the background medium through which a lighter, less viscous fluid buoyantly rises. If the interior fluid is continuously injected, a deformable pipe forms. The long wave interfacial dynamics are well-described by a dispersive nonlinear partial differential equation called the conduit equation.

Experiments, numerics, and asymptotics of the viscous fluid conduit system will be presented. Structures at multiple length scales are characterized, including solitary waves, periodic waves, and dispersive shock waves. A more generic class of large-scale disturbances is also studied and found to emit solitary waves whose number and amplitudes can be obtained. Of particular interest is the interaction of structures of different scales, such as solitary waves and dispersive shock waves. In the development of these theories for the conduit equation, we have uncovered asymptotic methods that are applicable to a wide range of dispersive hydrodynamic systems.

The conduit equation is nonintegrable, so exact methods such as the inverse scattering transform cannot be implemented. Instead, approximations of the conduit equation are studied, including the Whitham modulation equations, which can be derived for any dispersive hydrodynamic system with a periodic wave solution family and at least two conservation laws. The combination of the conduit equation's tractability and the relative ease of the associated experiments make this a model system for studying a wide range of dispersive hydrodynamic phenomena.

Indexing (document details)
Advisor: Hoefer, Mark A.
Commitee: Appelo, Daniel E., Crimaldi, John P., El, Gennady A., Julien, Keith
School: University of Colorado at Boulder
Department: Applied Mathematics
School Location: United States -- Colorado
Source: DAI-B 80/09(E), Dissertation Abstracts International
Subjects: Applied Mathematics
Keywords: Dispersive hydrodynamics, Dispersive shock waves, Nonlinear waves, Soliton fission, Solitons
Publication Number: 13856836
ISBN: 978-1-392-16492-1
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