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.
Categories: physics.flu-dyn physics.ao-ph