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VOLUME 92 | ISSUE 3 | PAGE 162
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
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.

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