Quasi-planar steep water waves

Abstract

A new description for highly nonlinear potential water waves is suggested, where weak 3D effects are included as small corrections to exact 2D equations written in conformal variables. Contrary to the traditional approach, a small parameter in this theory is not the surface slope, but it is the ratio of a typical wave length to a large transversal scale along the second horizontal coordinate. A first-order correction for the Hamiltonian functional is calculated, and the corresponding equations of motion are derived for steep water waves over an arbitrary inhomogeneous quasi-1D bottom profile.

revtex4, 4 pages, no figures

References in corpus (4)

• Weak Turbulent Kolmogorov Spectrum for Surface Gravity Waves
• Water waves over a strongly undulating bottom
• On Optimal Canonical Variables in the Theory of Ideal Fluid with Free Surface
• Toroidal bubbles with circulation in ideal hydrodynamics. A variational approach

Cited by in corpus (8)

• Nonlinear stage of the Benjamin-Feir instability: Three-dimensional coherent structures and rogue waves
• "Breathing" rogue wave observed in numerical experiment
• Non-Canonical Hamiltonian Structure and Poisson Bracket for 2D Hydrodynamics with Free Surface
• Enhanced rise of rogue waves in slant wave groups
• Numerical modeling of quasiplanar giant water waves
• Two different kinds of rogue waves in weakly-crossing sea states
• Canonical variables for steep planar water waves over nonuniform bed
• Water wave collapses over quasi-one-dimensional non-uniformly periodic bed profiles