On the Hamiltonian and geometric structure of Langmuir circulation

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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Main Author: Yang, Cheng
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2023
Subjects:
Science::Mathematics
Langmuir Circulation
Craik-Leibovich Equation
Online Access:https://hdl.handle.net/10356/171171
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Institution: Nanyang Technological University
Language: English
id sg-ntu-dr.10356-171171
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spelling sg-ntu-dr.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
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Science::Mathematics
Langmuir Circulation
Craik-Leibovich Equation
spellingShingle Science::Mathematics
Langmuir Circulation
Craik-Leibovich Equation
Yang, Cheng
On the Hamiltonian and geometric structure of Langmuir circulation
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.
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Yang, Cheng
format Article
author Yang, Cheng
author_sort Yang, Cheng
title On the Hamiltonian and geometric structure of Langmuir circulation
title_short 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_sort on the hamiltonian and geometric structure of langmuir circulation
publishDate 2023
url https://hdl.handle.net/10356/171171
_version_ 1781793734169460736

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