Nonlinear interfacial waves in a constant-vorticity planar flow over variable depth
V. P. Ruban
L. D. Landau Institute for Theoretical Physics RAS, 119334 Moscow, Russia
Abstract
Exact Lagrangian in compact form is derived for planar internal waves in a two-fluid system
with a relatively small density jump (the Boussinesq limit taking place in real oceanic
conditions), in the presence of a background shear current of constant vorticity,
and over arbitrary bottom profile. Long-wave asymptotic approximations of higher orders
are derived from the exact Hamiltonian functional in a remarkably simple way, for two
different parametrizations of the interface shape.