Author

Junwei Sun

Graduation Semester and Year

2017

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

Yue Liu

Second Advisor

Gaik Ambartsoumian

Third Advisor

Guojun Liao

Fourth Advisor

Jianzhong Su

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 Niño phenomenon. However, based on β-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.

Keywords

Blow-up, Coriolis effect, Rotation-Camassa-Holm equation, Shallow water, Wave breaking

Disciplines

Mathematics | Physical Sciences and Mathematics

Comments

Degree granted by The University of Texas at Arlington

Included in

Mathematics Commons

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