On the modeling of equatorial shallow-water waves with the Coriolis effect

被引:4
|
作者
Hu, Tianqiao [1 ]
Liu, Yue [2 ,3 ]
机构
[1] Sichuan Univ, Dept Math, Chengdu 610064, Sichuan, Peoples R China
[2] Chongqing Univ, Dept Math & Stat, Chongqing 401331, Peoples R China
[3] Univ Texas Arlington, Dept Math, Arlington, TX 76019 USA
关键词
Two component Camassa-Holm system; Coriolis force; Shallow-water wave; Wave-breaking; Global existence; BLOW-UP PHENOMENA; GLOBAL EXISTENCE; BREAKING WAVES; SOLITARY WAVES; CAMASSA; EQUATION; DERIVATION;
D O I
10.1016/j.physd.2018.12.002
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In the present study a simplified phenomenological model of shallow-water wave propagating mainly in the equatorial ocean regions with the Coriolis effect caused by the Earth's rotation is formally derived. The model equation which is analogous to the Green-Naghdi equations with the second-order approximation of the Camassa-Holm scaling captures stronger nonlinear effects than the classical dispersive integrable equations like the Korteweg-de Vries and two-component Camassa-Holm system. The local wellposedness of the Cauchy problem is then established by the linear transport theory and wave-breaking phenomenon is investigated based on the method of characteristics and the Riccati-type differential inequality. Finally, the condition of permanent waves is demonstrated by analyzing competition between the slope of average of horizontal velocity component and the free surface component. (C) 2018 Elsevier B.V. All rights reserved.
引用
收藏
页码:87 / 110
页数:24
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