On the Hamiltonian and geometric structure of Langmuir circulation
The Craik-Leibovich equation (CL) serves as the theoretical model for Langmuir circulation. We show that the CL equation can be reduced to the dual space of a certain Lie algebra central extension. On this space, the CL equation can be rewritten as a Hamiltonian equation corresponding to the kinetic...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-03-01
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| Series: | Communications in Analysis and Mechanics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/cam.2023004?viewType=HTML |
| _version_ | 1827391291978153984 |
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| author | Cheng Yang |
| author_facet | Cheng Yang |
| author_sort | Cheng Yang |
| collection | DOAJ |
| description | The Craik-Leibovich equation (CL) serves as the theoretical model for Langmuir circulation. We show that the CL equation can be reduced to the dual space of a certain Lie algebra central extension. On this space, the CL equation can be rewritten as a Hamiltonian equation corresponding to the kinetic energy. Additionally, we provide an explanation of the appearance of this central extension structure through an averaging theory for Langmuir circulation. Lastly, we prove a stability theorem for two-dimensional steady flows of the CL equation. The paper also contains two examples of stable steady CL flows. |
| first_indexed | 2024-03-08T17:08:21Z |
| format | Article |
| id | doaj.art-a06bc8f557dc48a2884d870b0e0bcde0 |
| institution | Directory Open Access Journal |
| issn | 2836-3310 |
| language | English |
| last_indexed | 2024-03-08T17:08:21Z |
| publishDate | 2023-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Communications in Analysis and Mechanics |
| spelling | doaj.art-a06bc8f557dc48a2884d870b0e0bcde02024-01-04T03:27:08ZengAIMS PressCommunications in Analysis and Mechanics2836-33102023-03-01152586910.3934/cam.2023004On the Hamiltonian and geometric structure of Langmuir circulationCheng Yang 0Division of Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, 637371, SingaporeThe Craik-Leibovich equation (CL) serves as the theoretical model for Langmuir circulation. We show that the CL equation can be reduced to the dual space of a certain Lie algebra central extension. On this space, the CL equation can be rewritten as a Hamiltonian equation corresponding to the kinetic energy. Additionally, we provide an explanation of the appearance of this central extension structure through an averaging theory for Langmuir circulation. Lastly, we prove a stability theorem for two-dimensional steady flows of the CL equation. The paper also contains two examples of stable steady CL flows.https://www.aimspress.com/article/doi/10.3934/cam.2023004?viewType=HTMLlangmuir circulationcraik-leibovich equationeuler equationcentral extensionhamiltonian structurestability |
| spellingShingle | Cheng Yang On the Hamiltonian and geometric structure of Langmuir circulation Communications in Analysis and Mechanics langmuir circulation craik-leibovich equation euler equation central extension hamiltonian structure stability |
| title | On the Hamiltonian and geometric structure of Langmuir circulation |
| title_full | On the Hamiltonian and geometric structure of Langmuir circulation |
| title_fullStr | On the Hamiltonian and geometric structure of Langmuir circulation |
| title_full_unstemmed | On the Hamiltonian and geometric structure of Langmuir circulation |
| title_short | On the Hamiltonian and geometric structure of Langmuir circulation |
| title_sort | on the hamiltonian and geometric structure of langmuir circulation |
| topic | langmuir circulation craik-leibovich equation euler equation central extension hamiltonian structure stability |
| url | https://www.aimspress.com/article/doi/10.3934/cam.2023004?viewType=HTML |
| work_keys_str_mv | AT chengyang onthehamiltonianandgeometricstructureoflangmuircirculation |