title: Canonical variables for steep planar water waves over nonuniform beds.
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 noncanonical conformal description of water waves over a strongly undulating bottom [V. P. Ruban, Phys. Rev. E 70, 066302 (2004)]. Also an alternative approach to the problem is discussed, which gives weakly nonlinear Hamiltonian models of different orders, both for free-surface waves and for interfacial waves.
authors.affiliation: Landau Institute for Theoretical Physics, 2 Kosygin Street, 119334 Moscow, Russia. ruban@itp.ac.ru
authors.forename: V P
authors.initials: VP
authors.lastname: Ruban