Subharmonic resonance of nonlinear cross-waves: Theory and experiments.

Persistent Link:
http://hdl.handle.net/10150/184350
Title:
Subharmonic resonance of nonlinear cross-waves: Theory and experiments.
Author:
Chen, Jerry Min.
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:
The generation and evolution of cross-waves in a channel are investigated analytically, numerically and experimentally. The derivation of the modulation equation governing the inviscid cross-wave amplitude yields the nonlinear Schrodinger equation with a homogeneous Robin boundary condition at the wavemaker. Either of two uniformly valid scalings--cross-wave amplitude of the same order as or much larger than the wavemaker amplitude--may be used in the derivations. The differences between the two scalings are discussed. The inviscid modulation equation is augmented by a linear damping term, the coefficient of which is determined empirically from the measured neutral stability curve. The viscous modulation equation is solved numerically. The theory is compared to experiments in a channel 30.9 cm wide, for mode n = 6, for frequencies close to the cutoff frequency 7.82 Hz. Measurements include the neutral stability curve, the onset of modulation, cross-wave phase along the channel, and cross-wave amplitude as functions of wavemaker amplitude, forcing frequency and distance from the wavemaker. These measurements are in good agreement with the numerical results. The results are also observed to be sensitive to viscous effects. Additionally, both numerical calculations and experiment reveal trapped and propagating modes. The trapped mode is most easily observed at positive detuning.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Resonance.; Waves.
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.titleSubharmonic resonance of nonlinear cross-waves: Theory and experiments.en_US
dc.creatorChen, Jerry Min.en_US
dc.contributor.authorChen, Jerry Min.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.abstractThe generation and evolution of cross-waves in a channel are investigated analytically, numerically and experimentally. The derivation of the modulation equation governing the inviscid cross-wave amplitude yields the nonlinear Schrodinger equation with a homogeneous Robin boundary condition at the wavemaker. Either of two uniformly valid scalings--cross-wave amplitude of the same order as or much larger than the wavemaker amplitude--may be used in the derivations. The differences between the two scalings are discussed. The inviscid modulation equation is augmented by a linear damping term, the coefficient of which is determined empirically from the measured neutral stability curve. The viscous modulation equation is solved numerically. The theory is compared to experiments in a channel 30.9 cm wide, for mode n = 6, for frequencies close to the cutoff frequency 7.82 Hz. Measurements include the neutral stability curve, the onset of modulation, cross-wave phase along the channel, and cross-wave amplitude as functions of wavemaker amplitude, forcing frequency and distance from the wavemaker. These measurements are in good agreement with the numerical results. The results are also observed to be sensitive to viscous effects. Additionally, both numerical calculations and experiment reveal trapped and propagating modes. The trapped mode is most easily observed at positive detuning.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectResonance.en_US
dc.subjectWaves.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.committeememberFasel, Hermann F.en_US
dc.contributor.committeememberLamb, George L.en_US
dc.contributor.committeememberPearlstein, Arne J.en_US
dc.identifier.proquest8814219en_US
dc.identifier.oclc701248771en_US
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