Steady periodic waves and formal stability for fixed-depth rotational equatorial flows

被引：16

作者：

Chu, Jifeng ^{[1
]}

Ding, Qixing ^{[1
]}

Yang, Yanjuan ^{[2
]}

机构：

[1] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China

[2] Hohai Univ, Dept Math, Nanjing 210098, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2020年 / 269卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Steady periodic waves; Rotational equatorial flows; Fixed-depth; Dispersion relation; Formal stability; GRAVITY WATER-WAVES; DISPERSION-RELATIONS; VARIATIONAL FORMULATIONS; ANALYTICITY; PRINCIPLE; SYMMETRY;

D O I：

10.1016/j.jde.2020.03.040

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we apply the bifurcation theory to study the steady two-dimensional periodic equatorial water waves for the f-plane approximation. We consider the waves with vorticity which propagate with a specified fixed depth between the thermocline and the upper boundary of the centre layer. Moreover, we present a functional J and its first variation corresponds to the exact equations in the transformed variables. Using the second variation of J, we prove a formal stability result for the bifurcation inducing the laminar solution. (c) 2020 Elsevier Inc. All rights reserved.

引用

页码：4192 / 4214

页数：23

共 24 条

[21] Approximations of steady periodic water waves in flows with constant vorticity
Constantin, A.
Kalimeris, K.
Scherzer, O.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2015, 25 : 276 - 306
[22] Pressure behavior and wave height estimates for steady periodic equatorial water waves
Li, Qixiang
Wang, Jinrong
APPLICABLE ANALYSIS, 2025,
[23] Variational Formulation of Rotational Steady Water Waves in Two-Layer Flows
Jifeng Chu
Qixing Ding
Joachim Escher
Journal of Mathematical Fluid Mechanics, 2021, 23
[24] On rotational flows with discontinuous vorticity beneath steady water waves near stagnation
Chen, Lin
Basu, Biswajit
Martin, Calin-, I
JOURNAL OF FLUID MECHANICS, 2021, 912

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