Canonical variables for steep planar water waves over nonuniform bed
arXiv:1002.2848 · doi:10.1103/PhysRevE.81.056303
Abstract
An explicit expression in terms of canonical variables is obtained for the Hamiltonian functional determining the fully nonlinear dynamics of two-dimensional potential flows of an ideal fluid with a free surface over an arbitrary nonuniform depth. The canonically conjugate variables are derived from the previously developed non-canonical conformal description of water waves over a strongly undulating bottom [V. P. Ruban, Phys. Rev. E {\bf 70}, 066302 (2004)]. Also an alternative approach to the problem is discussed, which gives weakly nonlinear Hamiltonian models of different orders.
revtex, 4.5 pages
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