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 |
| Published: |
2023
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| Online Access: | https://hdl.handle.net/10356/171171 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | 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. |
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