Transitions to chaotic cross-waves: An experimental investigation.

Persistent Link:
http://hdl.handle.net/10150/185144
Title:
Transitions to chaotic cross-waves: An experimental investigation.
Author:
Underhill, William Brian.
Issue Date:
1990
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:
Experiments were carried out to investigate the modulated nature of cross-waves in a long, deep, rectangular channel with a plane-flap type wavemaker at one end. Poincare sections, power spectra, Lyapunov exponents, correlation dimensions and winding numbers were generated from local wave height data to reveal the temporal behavior of modulated states. Information about the transverse spatial structure was obtained from digital image processing and multiprobe techniques. In general, three frequencies were observed: the subharmonic and two slow modulation frequencies. A one-mode modulation was associated with streamwise variation, and a sloshing modulation was associated with spanwise variation. The interaction of the oscillations produced a pattern of overlapping frequency-locked tongues in parameter space. In some tongues, all three frequencies were locked. The frequency-locked tongues had winding numbers in Farey tree sequences, and the overall picture was similar to the Arnold tongues of one-dimensional circle maps. Near the intersection of the neutral stability curves for two adjacent modes, a standing wave localized on one side of the tank was observed, in agreement with the coupled mode analysis of Ayanle (1989). At large forcing amplitudes or negative detunings, the transverse sloshing motion broke up into more than one soliton-like structure propagating in the spanwise direction and reflected by the sidewalls.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Engineering; Physics.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Aerospace and Mechanical Engineering; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Lichter, Seth

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleTransitions to chaotic cross-waves: An experimental investigation.en_US
dc.creatorUnderhill, William Brian.en_US
dc.contributor.authorUnderhill, William Brian.en_US
dc.date.issued1990en_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.abstractExperiments were carried out to investigate the modulated nature of cross-waves in a long, deep, rectangular channel with a plane-flap type wavemaker at one end. Poincare sections, power spectra, Lyapunov exponents, correlation dimensions and winding numbers were generated from local wave height data to reveal the temporal behavior of modulated states. Information about the transverse spatial structure was obtained from digital image processing and multiprobe techniques. In general, three frequencies were observed: the subharmonic and two slow modulation frequencies. A one-mode modulation was associated with streamwise variation, and a sloshing modulation was associated with spanwise variation. The interaction of the oscillations produced a pattern of overlapping frequency-locked tongues in parameter space. In some tongues, all three frequencies were locked. The frequency-locked tongues had winding numbers in Farey tree sequences, and the overall picture was similar to the Arnold tongues of one-dimensional circle maps. Near the intersection of the neutral stability curves for two adjacent modes, a standing wave localized on one side of the tank was observed, in agreement with the coupled mode analysis of Ayanle (1989). At large forcing amplitudes or negative detunings, the transverse sloshing motion broke up into more than one soliton-like structure propagating in the spanwise direction and reflected by the sidewalls.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectEngineeringen_US
dc.subjectPhysics.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineAerospace and Mechanical Engineeringen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorLichter, Sethen_US
dc.contributor.committeememberPeterson, Robert A.en_US
dc.contributor.committeememberPearlstein, Arne J.en_US
dc.contributor.committeememberSellers, Williamen_US
dc.contributor.committeememberZehnder, Josephen_US
dc.identifier.proquest9100561en_US
dc.identifier.oclc708653569en_US
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