dc.creator Sun, Junwei dc.date.accessioned 2017-10-02T14:48:49Z dc.date.available 2017-10-02T14:48:49Z dc.date.created 2017-08 dc.date.issued 2017-08-28 dc.date.submitted August 2017 dc.identifier.uri http://hdl.handle.net/10106/26989 dc.description.abstract The 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.mimetype application/pdf dc.language.iso en_US dc.subject Blow-up dc.subject Coriolis effect dc.subject rotation-Camassa-Holm equation dc.subject shallow water dc.subject wave breaking dc.title A STUDY ON THE NONLOCAL SHALLOW-WATER MODEL ARISING FROM THE FULL WATER WAVES WITH THE CORIOLIS EFFECT dc.type Thesis dc.contributor.committeeMember Liu, Yue dc.contributor.committeeMember Ambartsoumian, Gaik dc.contributor.committeeMember Liao, Guojun dc.contributor.committeeMember Su, Jianzhong dc.date.updated 2017-10-02T14:50:56Z thesis.degree.department Mathematics thesis.degree.grantor The University of Texas at Arlington thesis.degree.level Doctoral thesis.degree.name Doctor of Philosophy in Mathematics dc.type.material text
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