Details
| Original language | English |
|---|---|
| Pages (from-to) | 534-547 |
| Number of pages | 14 |
| Journal | Advances in nonlinear analysis |
| Volume | 10 |
| Issue number | 1 |
| Early online date | 22 Aug 2020 |
| Publication status | Published - Jan 2021 |
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
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
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In: Advances in nonlinear analysis, Vol. 10, No. 1, 01.2021, p. 534-547.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Variational formulations of steady rotational equatorial waves
AU - Chu, Jifeng
AU - Escher, Joachim
N1 - 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 Universität Hannover.
PY - 2021/1
Y1 - 2021/1
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 - http://www.scopus.com/inward/record.url?scp=85094141428&partnerID=8YFLogxK
U2 - 10.1515/anona-2020-0146
DO - 10.1515/anona-2020-0146
M3 - Article
AN - SCOPUS:85094141428
VL - 10
SP - 534
EP - 547
JO - Advances in nonlinear analysis
JF - Advances in nonlinear analysis
SN - 2191-9496
IS - 1
ER -