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: | Journal Article |
| Language: | English |
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2023
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| Online Access: | https://hdl.handle.net/10356/171171 |
| _version_ | 1826116541508222976 |
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| author | Yang, Cheng |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Yang, Cheng |
| author_sort | Yang, Cheng |
| collection | NTU |
| 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 | 2024-10-01T04:13:24Z |
| format | Journal Article |
| id | ntu-10356/171171 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T04:13:24Z |
| publishDate | 2023 |
| record_format | dspace |
| spelling | ntu-10356/1711712023-10-16T15:35:47Z On the Hamiltonian and geometric structure of Langmuir circulation Yang, Cheng School of Physical and Mathematical Sciences Science::Mathematics Langmuir Circulation Craik-Leibovich Equation 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. Published version 2023-10-16T06:44:54Z 2023-10-16T06:44:54Z 2023 Journal Article Yang, C. (2023). On the Hamiltonian and geometric structure of Langmuir circulation. Communications in Analysis and Mechanics, 15(2), 58-69. https://dx.doi.org/10.3934/cam.2023004 2836-3310 https://hdl.handle.net/10356/171171 10.3934/cam.2023004 2-s2.0-85163131548 2 15 58 69 en Communications in Analysis and Mechanics © 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0). application/pdf |
| spellingShingle | Science::Mathematics Langmuir Circulation Craik-Leibovich Equation Yang, Cheng On the Hamiltonian and geometric structure of Langmuir circulation |
| 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 | Science::Mathematics Langmuir Circulation Craik-Leibovich Equation |
| url | https://hdl.handle.net/10356/171171 |
| work_keys_str_mv | AT yangcheng onthehamiltonianandgeometricstructureoflangmuircirculation |