Variational formulations of steady rotational equatorial waves

Jifeng Chu; Joachim Escher

doi:10.1515/anona-2020-0146

Variational formulations of steady rotational equatorial waves

Jifeng Chu
, Joachim Escher^*

^*Corresponding author for this work

Institute of Applied Mathematics

Shanghai Normal University

Research output: Contribution to journal › Article › Research › peer review

Abstract

When the vorticity is monotone with depth, we present a variational formulation for steady periodic water waves of the equatorial flow in the f-plane approximation, and show that the governing equations for this motion can be obtained by studying variations of a suitable energy functional -in terms of the stream function and the thermocline. We also compute the second variation of the constrained energy functional, which is related to the linear stability of steady water waves.

Original language	English
Pages (from-to)	534-547
Number of pages	14
Journal	Advances in nonlinear analysis
Volume	10
Issue number	1
E-pub ahead of print	22 Aug 2020
DOIs	https://doi.org/10.1515/anona-2020-0146 https://doi.org/10.15488/10605
Publication status	Published - Jan 2021

Keywords

Equatorial flows
Steady periodic water waves
Variational formulations
Vorticity

ASJC Scopus subject areas

Analysis

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10.1515/anona-2020-0146Licence: CC BY 4.0
10.15488/10605Licence: CC BY 4.0

Cite this

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title = "Variational formulations of steady rotational equatorial waves",

abstract = "When the vorticity is monotone with depth, we present a variational formulation for steady periodic water waves of the equatorial flow in the f-plane approximation, and show that the governing equations for this motion can be obtained by studying variations of a suitable energy functional -in terms of the stream function and the thermocline. We also compute the second variation of the constrained energy functional, which is related to the linear stability of steady water waves.",

keywords = "Equatorial flows, Steady periodic water waves, Variational formulations, Vorticity",

author = "Jifeng Chu and Joachim Escher",

note = "Funding Information: Jifeng Chu was supported by the Alexander von Humboldt-Stiftung of Germany, and the National Natural Science Foundation of China (Grants No. 11671118 and No. 11871273). The publication of this article was funded by the Open Access Fund of Leibniz Universit{\"a}t Hannover.",

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AU - Escher, Joachim

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PY - 2021/1

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N2 - When the vorticity is monotone with depth, we present a variational formulation for steady periodic water waves of the equatorial flow in the f-plane approximation, and show that the governing equations for this motion can be obtained by studying variations of a suitable energy functional -in terms of the stream function and the thermocline. We also compute the second variation of the constrained energy functional, which is related to the linear stability of steady water waves.

AB - When the vorticity is monotone with depth, we present a variational formulation for steady periodic water waves of the equatorial flow in the f-plane approximation, and show that the governing equations for this motion can be obtained by studying variations of a suitable energy functional -in terms of the stream function and the thermocline. We also compute the second variation of the constrained energy functional, which is related to the linear stability of steady water waves.

KW - Equatorial flows

KW - Steady periodic water waves

KW - Variational formulations

KW - Vorticity

UR - https://www.scopus.com/pages/publications/85094141428

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DO - 10.1515/anona-2020-0146

M3 - Article

AN - SCOPUS:85094141428

SN - 2191-9496

VL - 10

SP - 534

EP - 547

JO - Advances in nonlinear analysis

JF - Advances in nonlinear analysis

IS - 1

ER -

Variational formulations of steady rotational equatorial waves

Abstract

Keywords

ASJC Scopus subject areas

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