# Periodic patterns, linear instability symplectic structure and mean-flow dynamics for three-dimensional surface waves

@article{Bridges1996PeriodicPL, title={Periodic patterns, linear instability symplectic structure and mean-flow dynamics for three-dimensional surface waves}, author={Thomas J. Bridges}, journal={Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences}, year={1996}, volume={354}, pages={533 - 574} }

Space and time periodic waves at the two-dimensional surface of an irrotational inviscid fluid of finite depth are considered. The governing equations are shown to have a new formulation as a generalized Hamiltonian system on a multisymplectic structure where there is a distinct symplectic operator corresponding to each unbounded space direction and time. The wave-generated mean flow in this framework has an interesting characterization as drift along a group orbit. The theory has interesting… CONTINUE READING

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