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dc.creatorSun, Junwei
dc.date.accessioned2017-10-02T14:48:49Z
dc.date.available2017-10-02T14:48:49Z
dc.date.created2017-08
dc.date.issued2017-08-28
dc.date.submittedAugust 2017
dc.identifier.urihttp://hdl.handle.net/10106/26989
dc.description.abstractThe Equatorial Undercurrent is a significant feature of the geophysical waves near the equator, which is one of the key factors to explain El Ni\~{n}o phenomenon. However, based on $\beta$-plane approximation, the classical theory of geophysical waves ignored the vertical structure of the Equatorial Undercurrent. To obtain a better description of the equatorial waves, in this dissertation, I study the rotational-Camassa-Holm (R-CH) equation, which is a mathematical model of long-crested water waves near the equator, propagating mainly in one direction with the effect of Earth's rotation under the $f$-plane approximation. R-CH equation can be derived by following the formal asymptotic procedures. Such a model equation is analogous to the Camassa-Holm approximation of the two-dimensional incompressible and irrotational Euler equations and has a formal bi-Hamiltonian structure. Its solutions corresponding to physically relevant initial perturbations is more accurate on a much longer time scale. It is shown that the deviation of the free surface can be determined by the horizontal velocity at a certain depth in the second-order approximation. The effects of the Coriolis force caused by the Earth rotation and nonlocal higher nonlinearities on blow-up criteria and wave-breaking phenomena are also investigated.
dc.format.mimetypeapplication/pdf
dc.language.isoen_US
dc.subjectBlow-up
dc.subjectCoriolis effect
dc.subjectrotation-Camassa-Holm equation
dc.subjectshallow water
dc.subjectwave breaking
dc.titleA STUDY ON THE NONLOCAL SHALLOW-WATER MODEL ARISING FROM THE FULL WATER WAVES WITH THE CORIOLIS EFFECT
dc.typeThesis
dc.contributor.committeeMemberLiu, Yue
dc.contributor.committeeMemberAmbartsoumian, Gaik
dc.contributor.committeeMemberLiao, Guojun
dc.contributor.committeeMemberSu, Jianzhong
dc.date.updated2017-10-02T14:50:56Z
thesis.degree.departmentMathematics
thesis.degree.grantorThe University of Texas at Arlington
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy in Mathematics
dc.type.materialtext


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