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.
|Advisor:||Hoefer, Mark A.|
|Commitee:||Appelo, Daniel E., Crimaldi, John P., El, Gennady A., Julien, Keith|
|School:||University of Colorado at Boulder|
|School Location:||United States -- Colorado|
|Source:||DAI-B 80/09(E), Dissertation Abstracts International|
|Keywords:||Dispersive hydrodynamics, Dispersive shock waves, Nonlinear waves, Soliton fission, Solitons|
Copyright in each Dissertation and Thesis is retained by the author. All Rights Reserved
The supplemental file or files you are about to download were provided to ProQuest by the author as part of a
dissertation or thesis. The supplemental files are provided "AS IS" without warranty. ProQuest is not responsible for the
content, format or impact on the supplemental file(s) on our system. in some cases, the file type may be unknown or
may be a .exe file. We recommend caution as you open such files.
Copyright of the original materials contained in the supplemental file is retained by the author and your access to the
supplemental files is subject to the ProQuest Terms and Conditions of use.
Depending on the size of the file(s) you are downloading, the system may take some time to download them. Please be