dc.contributor.author Ogbonna, Christian Chukwuebuka dc.date.accessioned 2017-09-22 18:22:08 (GMT) dc.date.available 2017-09-22 18:22:08 (GMT) dc.date.issued 2017-09-22 dc.date.submitted 2017-09-20 dc.identifier.uri http://hdl.handle.net/10012/12438 dc.description.abstract The problem of nonlinear interactions of internal waves is solved using small-amplitude expansions beyond the traditional approximation; that is the horizontal component of the Earth’s rotation vector is included in our analysis. It is shown that higher harmonics are generated from the reflection of propagating internal waves from a uniform slope due to the nonlinear interactions between the incident and the reflected first harmonic, this nonlinear interaction is restricted to the region where the two beams meet. en A criterion for critical reflection is derived in 2-D which depends on the horizontal orientation of the bottom slope in the horizontal geographical plane. The inclusion of the non-traditional $\tilde{f}$ term significantly changes the dynamics of internal waves in the ocean particularly for near inertial waves and for weak stratification due largely to the presence of inertial and sub-inertial waves which are absent in the traditional approximation. We also discuss collisions of two beams with respect to two collision configurations (the same sign horizontal and the same sign vertical group velocity). Secondary beams with frequencies equal to the sum and in some cases the difference of the frequencies of colliding beams are generated in the vicinity of the collision region particularly for the same sign horizontal group velocity configuration. The predictions of the formation rule adopted in this thesis are illustrated by specific examples using Internal Gravity Wave (IGW) adapted numerical simulations. dc.language.iso en en dc.publisher University of Waterloo en dc.subject Geophysical Fluid Dynamics en dc.subject Internal Gravity Waves en dc.subject Small amplitude expansion en dc.title Non-linear Interactions between Internal Wave Beams: Beyond the Traditional Approximation. en dc.type Master Thesis en dc.pending false uws-etd.degree.department Applied Mathematics en uws-etd.degree.discipline Applied Mathematics en uws-etd.degree.grantor University of Waterloo en uws-etd.degree Master of Mathematics en uws.contributor.advisor Lamb, Kevin uws.contributor.affiliation1 Faculty of Mathematics en uws.published.city Waterloo en uws.published.country Canada en uws.published.province Ontario en uws.typeOfResource Text en uws.peerReviewStatus Unreviewed en uws.scholarLevel Graduate en
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