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We show that the governing equations for two-dimensional gravity water waves with constant non-zero vorticity have a nearly-Hamiltonian structure, which becomes Hamiltonian for steady waves.
Constantin, A., Ivanov, R. & Prodanov, E. (2008). Nearly-Hamiltonian Structure for Water Waves with constant vorticity. Journal of Mathematical Fluid Mechanics, vol. 10, no. 2, pg. 224-237. doi:10.1007/s00021-006-0230-x
Science Foundation Ireland, IRCSET