@article{Yang2023, 
author = {Cheng Yang},
title = {On the Hamiltonian and geometric structure of Langmuir circulation},
year = {2023},
journal = {Communications in Analysis and Mechanics},
volume = {15},
number = {2},
pages = {58-69},
keywords = {Langmuir circulation, Craik-Leibovich equation, Euler equation, central extension, Hamiltonian structure, stability},
url = {https://www.sciopen.com/article/10.3934/cam.2023004},
doi = {10.3934/cam.2023004},
abstract = {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.}
}