Persistent Link:
http://hdl.handle.net/10150/184441
Title:
Viscous cross-waves: Stability and bifurcation.
Author:
Kwok, Loong-Piu.
Issue Date:
1988
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
In the first part of this thesis, the nonlinear Schrodinger equation for inviscid cross-waves near onset is found to be modified by viscous linear damping and detuning. The accompanying boundary condition at the wavemaker is also modified by damping from the wavemaker meniscus. The relative contributions of the free-surface, sidewalls, bottom, and wavemaker viscous boundary layers are computed. It is shown that viscous dissipation due to the wavemaker meniscus breaks the symmetry of the neutral curve. In the second part, existence and stability of steady solutions to the nonlinear Schrodinger equation are examined numerically. It is found that at forcing frequency above a critical value, f(c), only one solution exists. However, below f(c), multiple steady solutions, the number of which is determined, are possible. This multiplicity leads to hysteresis for f < f(c), in agreement with observation. A Hopf bifurcation of the steady solutions is found. This bifurcation is compared with the transition from unmodulated to periodically modulated cross-waves observed experimentally.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Wave mechanics.; Wave-motion, Theory of.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Applied Mathematics; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Lamb, G. L.; Lichter, S. H.

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleViscous cross-waves: Stability and bifurcation.en_US
dc.creatorKwok, Loong-Piu.en_US
dc.contributor.authorKwok, Loong-Piu.en_US
dc.date.issued1988en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractIn the first part of this thesis, the nonlinear Schrodinger equation for inviscid cross-waves near onset is found to be modified by viscous linear damping and detuning. The accompanying boundary condition at the wavemaker is also modified by damping from the wavemaker meniscus. The relative contributions of the free-surface, sidewalls, bottom, and wavemaker viscous boundary layers are computed. It is shown that viscous dissipation due to the wavemaker meniscus breaks the symmetry of the neutral curve. In the second part, existence and stability of steady solutions to the nonlinear Schrodinger equation are examined numerically. It is found that at forcing frequency above a critical value, f(c), only one solution exists. However, below f(c), multiple steady solutions, the number of which is determined, are possible. This multiplicity leads to hysteresis for f < f(c), in agreement with observation. A Hopf bifurcation of the steady solutions is found. This bifurcation is compared with the transition from unmodulated to periodically modulated cross-waves observed experimentally.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectWave mechanics.en_US
dc.subjectWave-motion, Theory of.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineApplied Mathematicsen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorLamb, G. L.en_US
dc.contributor.advisorLichter, S. H.en_US
dc.contributor.committeememberSears, W. R.en_US
dc.contributor.committeememberMcLaughlin, D. W.en_US
dc.contributor.committeememberChen, C. F.en_US
dc.identifier.proquest8820132en_US
dc.identifier.oclc701250834en_US
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