Variational formulations of steady rotational equatorial waves
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 𝓗 in terms...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2020-08-01
|
| Series: | Advances in Nonlinear Analysis |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/anona-2020-0146 |
| _version_ | 1818738445216907264 |
|---|---|
| author | Chu Jifeng Escher Joachim |
| author_facet | Chu Jifeng Escher Joachim |
| author_sort | Chu Jifeng |
| collection | DOAJ |
| description | 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 𝓗 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. |
| first_indexed | 2024-12-18T01:09:03Z |
| format | Article |
| id | doaj.art-50852cebc9b74d63994caddb4bd409a0 |
| institution | Directory Open Access Journal |
| issn | 2191-9496 2191-950X |
| language | English |
| last_indexed | 2024-12-18T01:09:03Z |
| publishDate | 2020-08-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advances in Nonlinear Analysis |
| spelling | doaj.art-50852cebc9b74d63994caddb4bd409a02022-12-21T21:26:09ZengDe GruyterAdvances in Nonlinear Analysis2191-94962191-950X2020-08-0110153454710.1515/anona-2020-0146anona-2020-0146Variational formulations of steady rotational equatorial wavesChu Jifeng0Escher Joachim1Department of Mathematics, Shanghai Normal University, Shanghai, 200234, ChinaInstitute for Applied Mathematics, Leibniz Universität Hannover, Hannover, GermanyWhen 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 𝓗 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.https://doi.org/10.1515/anona-2020-0146steady periodic water wavesequatorial flowsvorticityvariational formulationsprimary 76b1535j6047j1576b03 |
| spellingShingle | Chu Jifeng Escher Joachim Variational formulations of steady rotational equatorial waves Advances in Nonlinear Analysis steady periodic water waves equatorial flows vorticity variational formulations primary 76b15 35j60 47j15 76b03 |
| title | Variational formulations of steady rotational equatorial waves |
| title_full | Variational formulations of steady rotational equatorial waves |
| title_fullStr | Variational formulations of steady rotational equatorial waves |
| title_full_unstemmed | Variational formulations of steady rotational equatorial waves |
| title_short | Variational formulations of steady rotational equatorial waves |
| title_sort | variational formulations of steady rotational equatorial waves |
| topic | steady periodic water waves equatorial flows vorticity variational formulations primary 76b15 35j60 47j15 76b03 |
| url | https://doi.org/10.1515/anona-2020-0146 |
| work_keys_str_mv | AT chujifeng variationalformulationsofsteadyrotationalequatorialwaves AT escherjoachim variationalformulationsofsteadyrotationalequatorialwaves |