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The Effects of the Earth's Rotation on Internal Wave Near-resonant Triads and Weakly Nonlinear Models

dc.contributor.authorHu, Youna
dc.date.accessioned2007-08-24T14:35:32Z
dc.date.available2007-08-24T14:35:32Z
dc.date.issued2007-08-24T14:35:32Z
dc.date.submitted2007-08-15
dc.description.abstractThis thesis investigates the effects of the earth's rotation on internal waves from two perspectives of nonlinear internal wave theory: near-resonant triads and weakly nonlinear models. We apply perturbation theory (multiple scale analysis) to the governing equations of internal waves and develop a near-resonant internal wave triad theory. This theory explains a resonant-like phenomenon in the numerical results obtained from simulating internal waves generated by tide topography interaction. Furthermore, we find that the inclusion of the earth's rotation (nonzero $f$) in the numerical runs leads to a very special type of resonance: parametric subharmonic instability. Through using perturbation expansion to solve separable solutions to the governing equations of internal waves, we derive a new rotation modified KdV equation (RMKdV). Of particular interest, the dispersion relation of the new equation obeys the exact dispersion relation for internal waves for both small and moderate wavenumbers ($k$). Thus this new RMKdV is able to model wea kly nonlinear internal waves with various wavenumbers ($k$), better than the Ostrovsky equation which fails at describing waves of small $k$.en
dc.identifier.urihttp://hdl.handle.net/10012/3180
dc.language.isoenen
dc.pendingfalseen
dc.publisherUniversity of Waterlooen
dc.subjectNear-resonant Internal Wave Triadsen
dc.subjectWeakly Nonlinear Models of Internal Wavesen
dc.subject.programApplied Mathematicsen
dc.titleThe Effects of the Earth's Rotation on Internal Wave Near-resonant Triads and Weakly Nonlinear Modelsen
dc.typeMaster Thesisen
uws-etd.degreeMaster of Mathematicsen
uws-etd.degree.departmentApplied Mathematicsen
uws.peerReviewStatusUnrevieweden
uws.scholarLevelGraduateen
uws.typeOfResourceTexten

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